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Chapter 11: Decimal Numbers and Operations

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

11.1 Decimal place value

Place value (the value a digit has because of its position) changes by a factor of 10 from one place to the next. In this section, the focus is Decimal place value.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In 483,726, what is the value of the first digit 4?

  1. Count the places from the right.
  2. The digit 4 is in the 100,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 400,000

Worked Example 2

Problem: In 5,904,218, what is the value of the first digit 5?

  1. Count the places from the right.
  2. The digit 5 is in the 1,000,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 5,000,000

Worked Example 3

Problem: In 72,050,601, what is the value of the first digit 7?

  1. Count the places from the right.
  2. The digit 7 is in the 10,000,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 70,000,000

Worked Example 4

Problem: In 908,004,315, what is the value of the first digit 9?

  1. Count the places from the right.
  2. The digit 9 is in the 100,000,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 900,000,000

Worked Example 5

Problem: In 1,250,700,049, what is the value of the first digit 1?

  1. Count the places from the right.
  2. The digit 1 is in the 1,000,000,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 1,000,000,000

Worked Example 6

Problem: In 64,999, what is the value of the first digit 6?

  1. Count the places from the right.
  2. The digit 6 is in the 10,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 60,000

Worked Example 7

Problem: In 7,305,040, what is the value of the first digit 7?

  1. Count the places from the right.
  2. The digit 7 is in the 1,000,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 7,000,000

Worked Example 8

Problem: In 800,080, what is the value of the first digit 8?

  1. Count the places from the right.
  2. The digit 8 is in the 100,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 800,000

Worked Example 9

Problem: In 39,640,125, what is the value of the first digit 3?

  1. Count the places from the right.
  2. The digit 3 is in the 10,000,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 30,000,000

Worked Example 10

Problem: In 999,999,999, what is the value of the first digit 9?

  1. Count the places from the right.
  2. The digit 9 is in the 100,000,000 place.
  3. Multiply the digit by its place value.

Very beginner explanation: A digit's value depends on where it appears in the number.

Answer: 900,000,000

Practice exercise

Create one new Grade 8 problem involving Decimal place value. Show the important steps, include units when needed, and explain how you checked the answer.

11.2 Comparing decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Comparing decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Which is greater: 3.6 or 0.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 3.6

Worked Example 2

Problem: Which is greater: 8.25 or 1.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 8.25

Worked Example 3

Problem: Which is greater: 12.75 or 2.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 12.75

Worked Example 4

Problem: Which is greater: 0.96 or 0.3?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 0.96

Worked Example 5

Problem: Which is greater: 5.04 or 1.2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 5.04

Worked Example 6

Problem: Which is greater: 14.8 or 2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 14.8

Worked Example 7

Problem: Which is greater: 7.125 or 0.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 7.125

Worked Example 8

Problem: Which is greater: 20.05 or 3.75?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 20.05

Worked Example 9

Problem: Which is greater: 2.4 or 0.06?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 2.4

Worked Example 10

Problem: Which is greater: 100.5 or 4.02?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 100.5

Practice exercise

Create one new Grade 8 problem involving Comparing decimals. Show the important steps, include units when needed, and explain how you checked the answer.

11.3 Ordering decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Ordering decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Which is greater: 3.6 or 0.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 3.6

Worked Example 2

Problem: Which is greater: 8.25 or 1.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 8.25

Worked Example 3

Problem: Which is greater: 12.75 or 2.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 12.75

Worked Example 4

Problem: Which is greater: 0.96 or 0.3?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 0.96

Worked Example 5

Problem: Which is greater: 5.04 or 1.2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 5.04

Worked Example 6

Problem: Which is greater: 14.8 or 2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 14.8

Worked Example 7

Problem: Which is greater: 7.125 or 0.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 7.125

Worked Example 8

Problem: Which is greater: 20.05 or 3.75?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 20.05

Worked Example 9

Problem: Which is greater: 2.4 or 0.06?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 2.4

Worked Example 10

Problem: Which is greater: 100.5 or 4.02?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 100.5

Practice exercise

Create one new Grade 8 problem involving Ordering decimals. Show the important steps, include units when needed, and explain how you checked the answer.

11.4 Rounding decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Rounding decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Round 3.6 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 3.6

Worked Example 2

Problem: Round 8.25 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 8.2

Worked Example 3

Problem: Round 12.75 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 12.8

Worked Example 4

Problem: Round 0.96 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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 5

Problem: Round 5.04 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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

Worked Example 6

Problem: Round 14.8 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 14.8

Worked Example 7

Problem: Round 7.125 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 7.1

Worked Example 8

Problem: Round 20.05 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 20.1

Worked Example 9

Problem: Round 2.4 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 2.4

Worked Example 10

Problem: Round 100.5 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 100.5

Practice exercise

Create one new Grade 8 problem involving Rounding decimals. Show the important steps, include units when needed, and explain how you checked the answer.

11.5 Adding decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Adding decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 3.6 + 0.4.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 4

Worked Example 2

Problem: Calculate 8.25 + 1.5.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 9.75

Worked Example 3

Problem: Calculate 12.75 + 2.4.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 15.15

Worked Example 4

Problem: Calculate 0.96 + 0.3.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 1.26

Worked Example 5

Problem: Calculate 5.04 + 1.2.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 6.24

Worked Example 6

Problem: Calculate 14.8 + 2.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 16.8

Worked Example 7

Problem: Calculate 7.125 + 0.5.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 7.625

Worked Example 8

Problem: Calculate 20.05 + 3.75.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 23.8

Worked Example 9

Problem: Calculate 2.4 + 0.06.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 2.46

Worked Example 10

Problem: Calculate 100.5 + 4.02.

  1. Line up decimal points.
  2. Add by place value.
  3. Bring the decimal point straight down.

Very beginner explanation: Lining up decimal points keeps tenths with tenths, hundredths with hundredths, and so on.

Answer: 104.52

Practice exercise

Create one new Grade 8 problem involving Adding decimals. Show the important steps, include units when needed, and explain how you checked the answer.

11.6 Subtracting decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Subtracting decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 3.6 - 0.4.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 3.2

Worked Example 2

Problem: Calculate 8.25 - 1.5.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 6.75

Worked Example 3

Problem: Calculate 12.75 - 2.4.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 10.35

Worked Example 4

Problem: Calculate 0.96 - 0.3.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 0.66

Worked Example 5

Problem: Calculate 5.04 - 1.2.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 3.84

Worked Example 6

Problem: Calculate 14.8 - 2.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 12.8

Worked Example 7

Problem: Calculate 7.125 - 0.5.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 6.625

Worked Example 8

Problem: Calculate 20.05 - 3.75.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 16.3

Worked Example 9

Problem: Calculate 2.4 - 0.06.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 2.34

Worked Example 10

Problem: Calculate 100.5 - 4.02.

  1. Line up decimal points.
  2. Add zeros if helpful.
  3. Subtract by place value.

Very beginner explanation: Zeros to the right of a decimal do not change its value, so they can help line up places.

Answer: 96.48

Practice exercise

Create one new Grade 8 problem involving Subtracting decimals. Show the important steps, include units when needed, and explain how you checked the answer.

11.7 Multiplying decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Multiplying decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 3.6 × 0.4.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 1.44

Worked Example 2

Problem: Calculate 8.25 × 1.5.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 12.375

Worked Example 3

Problem: Calculate 12.75 × 2.4.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 30.6

Worked Example 4

Problem: Calculate 0.96 × 0.3.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 0.288

Worked Example 5

Problem: Calculate 5.04 × 1.2.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 6.048

Worked Example 6

Problem: Calculate 14.8 × 2.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 29.6

Worked Example 7

Problem: Calculate 7.125 × 0.5.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 3.5625

Worked Example 8

Problem: Calculate 20.05 × 3.75.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 75.1875

Worked Example 9

Problem: Calculate 2.4 × 0.06.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 0.144

Worked Example 10

Problem: Calculate 100.5 × 4.02.

  1. Multiply as if the numbers were whole numbers.
  2. Count the total decimal places in both factors.
  3. Place the decimal in the product.

Very beginner explanation: The decimal position in a product is determined by the total decimal places in the factors.

Answer: 404.01

Practice exercise

Create one new Grade 8 problem involving Multiplying decimals. Show the important steps, include units when needed, and explain how you checked the answer.

11.8 Dividing decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Dividing decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 3.6 ÷ 0.4.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 9

Worked Example 2

Problem: Calculate 8.25 ÷ 1.5.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 5.5

Worked Example 3

Problem: Calculate 12.75 ÷ 2.4.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 5.3125

Worked Example 4

Problem: Calculate 0.96 ÷ 0.3.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 3.2

Worked Example 5

Problem: Calculate 5.04 ÷ 1.2.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 4.2

Worked Example 6

Problem: Calculate 14.8 ÷ 2.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 7.4

Worked Example 7

Problem: Calculate 7.125 ÷ 0.5.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 14.25

Worked Example 8

Problem: Calculate 20.05 ÷ 3.75.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 5.3467

Worked Example 9

Problem: Calculate 2.4 ÷ 0.06.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 40

Worked Example 10

Problem: Calculate 100.5 ÷ 4.02.

  1. If the divisor has a decimal, move its decimal to make it whole.
  2. Move the dividend decimal the same number of places.
  3. Divide normally.

Very beginner explanation: Moving both decimals by the same power of 10 keeps the quotient unchanged.

Answer: 25

Practice exercise

Create one new Grade 8 problem involving Dividing decimals. Show the important steps, include units when needed, and explain how you checked the answer.

11.9 Multiplying by powers of 10

Multiplying by powers of 10 is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 4.5e+06 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 4.5 × 10^6

Worked Example 2

Problem: Write 72000 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 7.2 × 10^4

Worked Example 3

Problem: Write 0.0032 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 3.2 × 10^-3

Worked Example 4

Problem: Write 9.8e+08 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 9.8 × 10^8

Worked Example 5

Problem: Write 4.5e-05 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 4.5 × 10^-5

Worked Example 6

Problem: Write 6.25e+09 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 6.25 × 10^9

Worked Example 7

Problem: Write 8.1e-07 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 8.1 × 10^-7

Worked Example 8

Problem: Write 35700 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 3.57 × 10^4

Worked Example 9

Problem: Write 0.092 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 9.2 × 10^-2

Worked Example 10

Problem: Write 1.2e+06 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 1.2 × 10^6

Practice exercise

Create one new Grade 8 problem involving Multiplying by powers of 10. Show the important steps, include units when needed, and explain how you checked the answer.

11.10 Dividing by powers of 10

Dividing by powers of 10 is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 4.5e+06 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 4.5 × 10^6

Worked Example 2

Problem: Write 72000 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 7.2 × 10^4

Worked Example 3

Problem: Write 0.0032 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 3.2 × 10^-3

Worked Example 4

Problem: Write 9.8e+08 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 9.8 × 10^8

Worked Example 5

Problem: Write 4.5e-05 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 4.5 × 10^-5

Worked Example 6

Problem: Write 6.25e+09 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 6.25 × 10^9

Worked Example 7

Problem: Write 8.1e-07 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 8.1 × 10^-7

Worked Example 8

Problem: Write 35700 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 3.57 × 10^4

Worked Example 9

Problem: Write 0.092 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 9.2 × 10^-2

Worked Example 10

Problem: Write 1.2e+06 in scientific notation.

  1. Move the decimal so exactly one non-zero digit is before it.
  2. Count how many places the decimal moved.
  3. Moving left gives a positive exponent; moving right gives a negative exponent.

Very beginner explanation: Scientific notation is a compact way to represent extremely large or small numbers.

Answer: 1.2 × 10^6

Practice exercise

Create one new Grade 8 problem involving Dividing by powers of 10. Show the important steps, include units when needed, and explain how you checked the answer.

11.11 Estimating decimal calculations

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Estimating decimal calculations.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Round 3.6 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 3.6

Worked Example 2

Problem: Round 8.25 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 8.2

Worked Example 3

Problem: Round 12.75 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 12.8

Worked Example 4

Problem: Round 0.96 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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 5

Problem: Round 5.04 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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

Worked Example 6

Problem: Round 14.8 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 14.8

Worked Example 7

Problem: Round 7.125 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 7.1

Worked Example 8

Problem: Round 20.05 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 20.1

Worked Example 9

Problem: Round 2.4 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 2.4

Worked Example 10

Problem: Round 100.5 to the nearest tenth.

  1. Locate the tenths digit.
  2. Look at the hundredths digit.
  3. Round the tenths digit 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: 100.5

Practice exercise

Create one new Grade 8 problem involving Estimating decimal calculations. Show the important steps, include units when needed, and explain how you checked the answer.

11.12 Money applications

Money applications is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Which is greater: 3.6 or 0.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 3.6

Worked Example 2

Problem: Which is greater: 8.25 or 1.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 8.25

Worked Example 3

Problem: Which is greater: 12.75 or 2.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 12.75

Worked Example 4

Problem: Which is greater: 0.96 or 0.3?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 0.96

Worked Example 5

Problem: Which is greater: 5.04 or 1.2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 5.04

Worked Example 6

Problem: Which is greater: 14.8 or 2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 14.8

Worked Example 7

Problem: Which is greater: 7.125 or 0.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 7.125

Worked Example 8

Problem: Which is greater: 20.05 or 3.75?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 20.05

Worked Example 9

Problem: Which is greater: 2.4 or 0.06?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 2.4

Worked Example 10

Problem: Which is greater: 100.5 or 4.02?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 100.5

Practice exercise

Create one new Grade 8 problem involving Money applications. Show the important steps, include units when needed, and explain how you checked the answer.

11.13 Measurement applications

Measurement applications is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Which is greater: 3.6 or 0.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 3.6

Worked Example 2

Problem: Which is greater: 8.25 or 1.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 8.25

Worked Example 3

Problem: Which is greater: 12.75 or 2.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 12.75

Worked Example 4

Problem: Which is greater: 0.96 or 0.3?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 0.96

Worked Example 5

Problem: Which is greater: 5.04 or 1.2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 5.04

Worked Example 6

Problem: Which is greater: 14.8 or 2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 14.8

Worked Example 7

Problem: Which is greater: 7.125 or 0.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 7.125

Worked Example 8

Problem: Which is greater: 20.05 or 3.75?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 20.05

Worked Example 9

Problem: Which is greater: 2.4 or 0.06?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 2.4

Worked Example 10

Problem: Which is greater: 100.5 or 4.02?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 100.5

Practice exercise

Create one new Grade 8 problem involving Measurement applications. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 11 Review Questions and Answers

Q1. What is important to remember about Decimal place value?

Answer: Place value (the value a digit has because of its position) changes by a factor of 10 from one place to the next. In this section, the focus is Decimal place value.

Q2. What is important to remember about Comparing decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Comparing decimals.

Q3. What is important to remember about Ordering decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Ordering decimals.

Q4. What is important to remember about Rounding decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Rounding decimals.

Q5. What is important to remember about Adding decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Adding decimals.

Q6. What is important to remember about Subtracting decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Subtracting decimals.

Q7. What is important to remember about Multiplying decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Multiplying decimals.

Q8. What is important to remember about Dividing decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Dividing decimals.

Q9. What is important to remember about Multiplying by powers of 10?

Answer: Multiplying by powers of 10 is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q10. What is important to remember about Dividing by powers of 10?

Answer: Dividing by powers of 10 is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q11. What is important to remember about Estimating decimal calculations?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Estimating decimal calculations.

Q12. What is important to remember about Money applications?

Answer: Money applications is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Measurement applications?

Answer: Measurement applications is an important Grade 8 concept in Decimal Numbers and Operations. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q16. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer was obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q26. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q27. Why compare more than one strategy?

Answer: Different strategies may make a problem easier and provide a way to verify the result.

Q28. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q29. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.