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Chapter 5: Decimals to Hundredths

Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 5Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Decimals to Hundredths with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

  • Tenths and hundredths (a Grade 5 idea used in this chapter)
  • Decimal place-value charts (a Grade 5 idea used in this chapter)
  • Reading decimals (a Grade 5 idea used in this chapter)
  • Writing decimals in standard form (a Grade 5 idea used in this chapter)
  • Writing decimals in word form (a Grade 5 idea used in this chapter)
  • Representing decimals with models (a Grade 5 idea used in this chapter)
  • Decimals on number lines (a Grade 5 idea used in this chapter)
  • Equivalent decimals such as 0.5 and 0.50 (a Grade 5 idea used in this chapter)
  • Connecting decimals to money (a Grade 5 idea used in this chapter)
  • Connecting decimals to metric measurement (a Grade 5 idea used in this chapter)

How to Learn This Chapter

Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

5.1 Tenths and hundredths

Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Tenths and hundredths?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Tenths and hundredths?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Tenths and hundredths.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Tenths and hundredths problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Tenths and hundredths.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Tenths and hundredths can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Round 3.75 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 3.8

Worked Example 7

Problem: Round 8.4 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 8.4

Worked Example 8

Problem: Round 12.05 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 12.1

Worked Example 9

Problem: Round 0.96 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 1

Worked Example 10

Problem: Round 5.125 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 5.1

Practice Exercise

Create one new question about Tenths and hundredths. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.2 Decimal place-value charts

Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Decimal place-value charts?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Decimal place-value charts?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Decimal place-value charts.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Decimal place-value charts problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Decimal place-value charts.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Decimal place-value charts can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Round 3.75 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 3.8

Worked Example 7

Problem: Round 8.4 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 8.4

Worked Example 8

Problem: Round 12.05 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 12.1

Worked Example 9

Problem: Round 0.96 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 1

Worked Example 10

Problem: Round 5.125 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 5.1

Practice Exercise

Create one new question about Decimal place-value charts. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.3 Reading decimals

Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Reading decimals?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Reading decimals?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Reading decimals.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Reading decimals problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Reading decimals.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Reading decimals can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Round 3.75 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 3.8

Worked Example 7

Problem: Round 8.4 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 8.4

Worked Example 8

Problem: Round 12.05 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 12.1

Worked Example 9

Problem: Round 0.96 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 1

Worked Example 10

Problem: Round 5.125 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 5.1

Practice Exercise

Create one new question about Reading decimals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.4 Writing decimals in standard form

Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Writing decimals in standard form?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Worked Example 2

Problem: What should you identify first before solving a problem about Writing decimals in standard form?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Writing decimals in standard form.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Writing decimals in standard form problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Writing decimals in standard form.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Writing decimals in standard form can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: What is the value of the first digit in 638,420,715?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 600,000,000

Worked Example 7

Problem: What is the value of the first digit in 92,305,004?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 90,000,000

Worked Example 8

Problem: What is the value of the first digit in 704,090,650?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 700,000,000

Worked Example 9

Problem: What is the value of the first digit in 18,765,432?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 10,000,000

Worked Example 10

Problem: What is the value of the first digit in 999,500,001?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 900,000,000

Practice Exercise

Create one new question about Writing decimals in standard form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.5 Writing decimals in word form

Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Writing decimals in word form?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Worked Example 2

Problem: What should you identify first before solving a problem about Writing decimals in word form?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Writing decimals in word form.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Writing decimals in word form problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Writing decimals in word form.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Answer: Writing decimals in word form can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: What is the value of the first digit in 638,420,715?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 600,000,000

Worked Example 7

Problem: What is the value of the first digit in 92,305,004?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 90,000,000

Worked Example 8

Problem: What is the value of the first digit in 704,090,650?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 700,000,000

Worked Example 9

Problem: What is the value of the first digit in 18,765,432?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 10,000,000

Worked Example 10

Problem: What is the value of the first digit in 999,500,001?

  1. Find the position of the first digit.
  2. Multiply the digit by its place value.

Very beginner explanation: Place value tells the value of a digit because of where it is located.

Answer: 900,000,000

Practice Exercise

Create one new question about Writing decimals in word form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.6 Representing decimals with models

Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Representing decimals with models?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Representing decimals with models?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Representing decimals with models.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Representing decimals with models problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Representing decimals with models.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Representing decimals with models can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Round 3.75 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 3.8

Worked Example 7

Problem: Round 8.4 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 8.4

Worked Example 8

Problem: Round 12.05 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 12.1

Worked Example 9

Problem: Round 0.96 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 1

Worked Example 10

Problem: Round 5.125 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 5.1

Practice Exercise

Create one new question about Representing decimals with models. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.7 Decimals on number lines

Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Decimals on number lines?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Decimals on number lines?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Decimals on number lines.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Decimals on number lines problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Decimals on number lines.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Decimals on number lines can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Which is farther right on a number line: 3,000 or 3,750?

  1. Numbers get larger as you move right.
  2. 3,750 is greater than 3,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 3,750

Worked Example 7

Problem: Which is farther right on a number line: 4,000 or 4,750?

  1. Numbers get larger as you move right.
  2. 4,750 is greater than 4,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 4,750

Worked Example 8

Problem: Which is farther right on a number line: 5,000 or 5,750?

  1. Numbers get larger as you move right.
  2. 5,750 is greater than 5,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 5,750

Worked Example 9

Problem: Which is farther right on a number line: 6,000 or 6,750?

  1. Numbers get larger as you move right.
  2. 6,750 is greater than 6,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 6,750

Worked Example 10

Problem: Which is farther right on a number line: 7,000 or 7,750?

  1. Numbers get larger as you move right.
  2. 7,750 is greater than 7,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 7,750

Practice Exercise

Create one new question about Decimals on number lines. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.8 Equivalent decimals such as 0.5 and 0.50

Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Equivalent decimals such as 0.5 and 0.50?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Equivalent decimals such as 0.5 and 0.50?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Equivalent decimals such as 0.5 and 0.50.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Equivalent decimals such as 0.5 and 0.50 problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Equivalent decimals such as 0.5 and 0.50.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Equivalent decimals such as 0.5 and 0.50 can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Round 3.75 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 3.8

Worked Example 7

Problem: Round 8.4 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 8.4

Worked Example 8

Problem: Round 12.05 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 12.1

Worked Example 9

Problem: Round 0.96 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 1

Worked Example 10

Problem: Round 5.125 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 5.1

Practice Exercise

Create one new question about Equivalent decimals such as 0.5 and 0.50. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.9 Connecting decimals to money

Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Connecting decimals to money?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Connecting decimals to money?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Connecting decimals to money.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Connecting decimals to money problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Connecting decimals to money.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Connecting decimals to money can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Round 3.75 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 3.8

Worked Example 7

Problem: Round 8.4 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 8.4

Worked Example 8

Problem: Round 12.05 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 12.1

Worked Example 9

Problem: Round 0.96 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 1

Worked Example 10

Problem: Round 5.125 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 5.1

Practice Exercise

Create one new question about Connecting decimals to money. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.10 Connecting decimals to metric measurement

Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Connecting decimals to metric measurement?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Worked Example 2

Problem: What should you identify first before solving a problem about Connecting decimals to metric measurement?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Connecting decimals to metric measurement.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Connecting decimals to metric measurement problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Connecting decimals to metric measurement.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Answer: Connecting decimals to metric measurement can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Round 3.75 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 3.8

Worked Example 7

Problem: Round 8.4 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 8.4

Worked Example 8

Problem: Round 12.05 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 12.1

Worked Example 9

Problem: Round 0.96 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 1

Worked Example 10

Problem: Round 5.125 to the nearest tenth.

  1. Find the tenths digit.
  2. Look at the hundredths digit.
  3. Round up if the hundredths digit is 5 or more.

Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.

Answer: 5.1

Practice Exercise

Create one new question about Connecting decimals to metric measurement. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

Chapter Notes, Practice, and Common Mistakes

Chapter Notes

  • Read the question before calculating.
  • Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
  • Show the reasoning and check the final answer with a second method when possible.

Extra Practice

  1. Create and solve one original problem about Tenths and hundredths.
  2. Create and solve one original problem about Decimal place-value charts.
  3. Create and solve one original problem about Reading decimals.
  4. Create and solve one original problem about Writing decimals in standard form.
  5. Create and solve one original problem about Writing decimals in word form.
  6. Create and solve one original problem about Representing decimals with models.

Common Mistakes

  • Skipping the meaning and trying to memorize a rule only.
  • Using the wrong operation because the question was not read completely.
  • Ignoring units, labels, place values, or the context of the problem.
  • Not estimating or checking whether the final answer is reasonable.
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30 Review Questions and Answers

Q1. What is the key idea in Tenths and hundredths?

Answer: Tenths and hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q2. What is the key idea in Decimal place-value charts?

Answer: Decimal place-value charts uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q3. What is the key idea in Reading decimals?

Answer: Reading decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q4. What is the key idea in Writing decimals in standard form?

Answer: Writing decimals in standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Q5. What is the key idea in Writing decimals in word form?

Answer: Writing decimals in word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.

Q6. What is the key idea in Representing decimals with models?

Answer: Representing decimals with models uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q7. What is the key idea in Decimals on number lines?

Answer: Decimals on number lines uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q8. What is the key idea in Equivalent decimals such as 0.5 and 0.50?

Answer: Equivalent decimals such as 0.5 and 0.50 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q9. What is the key idea in Connecting decimals to money?

Answer: Connecting decimals to money uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q10. What is the key idea in Connecting decimals to metric measurement?

Answer: Connecting decimals to metric measurement uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.

Q11. Why should you estimate before or after a calculation?

Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.

Q12. Why are labels and units important?

Answer: They show what a number represents and help prevent mixing unlike quantities.

Q13. How can a diagram help solve a problem?

Answer: A diagram makes quantities and relationships visible before calculation.

Q14. How can inverse operations check an answer?

Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.

Q15. Why should you show steps?

Answer: Showing steps makes reasoning clear and helps find where an error happened.

Q16. What should you do after making a mistake?

Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.

Q17. How can a number line support reasoning?

Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.

Q18. When is a table useful?

Answer: A table organizes related values so patterns and comparisons are easier to see.

Q19. When is a graph useful?

Answer: A graph makes trends, comparisons, locations, or data patterns visible.

Q20. How do you decide which operation to use?

Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.

Q21. Why should you check place value?

Answer: A digit or decimal has a different value depending on its position.

Q22. What makes an answer reasonable?

Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.

Q23. How can you explain mathematical reasoning clearly?

Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.

Q24. Why can more than one strategy be correct?

Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.

Q25. How should you approach a difficult Grade 5 problem?

Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.

Q26. How can you practise Decimals to Hundredths effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q27. How can you practise Decimals to Hundredths effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q28. How can you practise Decimals to Hundredths effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q29. How can you practise Decimals to Hundredths effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q30. How can you practise Decimals to Hundredths effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.