Chapter 28: Decimal Patterns
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Decimal Patterns with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Unit Rate (a rate per one unit)
- Circle Graph (a graph using sectors of a circle to show parts of a whole)
- Exchange Rate (the value of one currency expressed in another currency)
- Interest Rate (percentage used to calculate interest)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
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.
28.1 Growing decimal patterns
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Growing decimal patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Growing decimal patterns .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Growing decimal patterns .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Growing decimal patterns .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Growing decimal patterns .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Growing decimal patterns .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Growing decimal patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.2 Shrinking decimal patterns
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Shrinking decimal patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Shrinking decimal patterns .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Shrinking decimal patterns .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Shrinking decimal patterns .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Shrinking decimal patterns .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Shrinking decimal patterns .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Shrinking decimal patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.3 Constant decimal rates
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Constant decimal rates .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Constant decimal rates .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Constant decimal rates .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Constant decimal rates .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Constant decimal rates .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Constant decimal rates .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Constant decimal rates. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.4 Finding decimal differences
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Finding decimal differences .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Finding decimal differences .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Finding decimal differences .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Finding decimal differences .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Finding decimal differences .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Finding decimal differences .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Finding decimal differences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.5 Extending decimal sequences
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Extending decimal sequences .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Extending decimal sequences .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Extending decimal sequences .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Extending decimal sequences .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Extending decimal sequences .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Extending decimal sequences .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Extending decimal sequences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.6 Writing decimal pattern rules
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Writing decimal pattern rules .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Writing decimal pattern rules .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Writing decimal pattern rules .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Writing decimal pattern rules .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Writing decimal pattern rules .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Writing decimal pattern rules .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Writing decimal pattern rules. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.7 Tables of decimal values
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Tables of decimal values .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Tables of decimal values .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Tables of decimal values .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Tables of decimal values .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Tables of decimal values .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Tables of decimal values .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Tables of decimal values. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.8 Graphs of decimal patterns
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Graphs of decimal patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Graphs of decimal patterns .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Graphs of decimal patterns .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Graphs of decimal patterns .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Graphs of decimal patterns .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Graphs of decimal patterns .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Graphs of decimal patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.9 Comparing whole-number and decimal patterns
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Comparing whole-number and decimal patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 487,305,219 and 487,292,874.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Comparing whole-number and decimal patterns .
Answer: 487,305,219 > 487,292,874
Worked Example 2
Problem: Compare 73,040,506 and 73,015,816.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Comparing whole-number and decimal patterns .
Answer: 73,040,506 > 73,015,816
Worked Example 3
Problem: Compare 905,600,012 and 905,562,977.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Comparing whole-number and decimal patterns .
Answer: 905,600,012 > 905,562,977
Worked Example 4
Problem: Compare 1,000,000,000 and 999,950,620.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Comparing whole-number and decimal patterns .
Answer: 1,000,000,000 > 999,950,620
Worked Example 5
Problem: Compare 268,999,450 and 268,937,725.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Comparing whole-number and decimal patterns .
Answer: 268,999,450 > 268,937,725
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Comparing whole-number and decimal patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.10 Money patterns
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Money patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Money patterns .
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Money patterns .
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Money patterns .
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Money patterns .
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Money patterns .
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Money patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.11 Measurement patterns
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Measurement patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Measurement patterns .
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Measurement patterns .
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Measurement patterns .
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Measurement patterns .
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Measurement patterns .
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Measurement patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
28.12 Real-life decimal sequences
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Real-life decimal sequences .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Real-life decimal sequences .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Real-life decimal sequences .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Real-life decimal sequences .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Real-life decimal sequences .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Real-life decimal sequences .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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.
- Find the tenths digit.
- Look at the hundredths digit.
- 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 Real-life decimal sequences. 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 complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Growing decimal patterns . Show your reasoning and check your answer.
- Create and solve a new question about Shrinking decimal patterns . Show your reasoning and check your answer.
- Create and solve a new question about Constant decimal rates . Show your reasoning and check your answer.
- Create and solve a new question about Finding decimal differences . Show your reasoning and check your answer.
- Create and solve a new question about Extending decimal sequences . Show your reasoning and check your answer.
- Create and solve a new question about Writing decimal pattern rules . Show your reasoning and check your answer.
- Create and solve a new question about Tables of decimal values . Show your reasoning and check your answer.
- Create and solve a new question about Graphs of decimal patterns . Show your reasoning and check your answer.
- Create and solve a new question about Comparing whole-number and decimal patterns . Show your reasoning and check your answer.
- Create and solve a new question about Money patterns . Show your reasoning and check your answer.
- Create and solve a new question about Measurement patterns . Show your reasoning and check your answer.
- Create and solve a new question about Real-life decimal sequences . Show your reasoning and check your answer.
Common Mistakes
- Combining unlike terms.
- Changing only one side of an equation.
- Forgetting to distribute to every term.
- Using a pattern rule that works only for the first few terms.
- Writing code without tracing variable values.
- Using a mathematical model without stating assumptions.
30 Review Questions and Answers
Q1. What is important to remember about Growing decimal patterns?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Growing decimal patterns.
Q2. What is important to remember about Shrinking decimal patterns?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Shrinking decimal patterns.
Q3. What is important to remember about Constant decimal rates?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Constant decimal rates.
Q4. What is important to remember about Finding decimal differences?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Finding decimal differences.
Q5. What is important to remember about Extending decimal sequences?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Extending decimal sequences.
Q6. What is important to remember about Writing decimal pattern rules?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Writing decimal pattern rules.
Q7. What is important to remember about Tables of decimal values?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Tables of decimal values.
Q8. What is important to remember about Graphs of decimal patterns?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Graphs of decimal patterns.
Q9. What is important to remember about Comparing whole-number and decimal patterns?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Comparing whole-number and decimal patterns.
Q10. What is important to remember about Money patterns?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Money patterns.
Q11. What is important to remember about Measurement patterns?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Measurement patterns.
Q12. What is important to remember about Real-life decimal sequences?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Real-life decimal sequences.
Q13. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q14. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q15. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q16. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q17. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q18. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q19. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q20. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q21. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q22. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q23. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q24. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q25. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q26. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q27. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q28. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q29. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.
Q30. Why should sources be checked in data problems?
Answer: Reliable sources and fair collection methods make conclusions more trustworthy.