Chapter 25: Decimal Tenths in Algebraic Expressions
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Decimal Tenths in Algebraic Expressions in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Decimal tenths in expressions (A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.)
- Money expressions (An algebraic expression combines numbers, variables, and operations without an equals sign.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
25.1 Decimal tenths in expressions
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What digit is in the tenths place of 47.258?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 2
Problem: What digit is in the tenths place of 3.217?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 3
Problem: What digit is in the tenths place of 61.098?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 0
Worked Example 4
Problem: What digit is in the tenths place of 30.708?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 7
Worked Example 5
Problem: What digit is in the tenths place of 19.43?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 4
Worked Example 6
Problem: What digit is in the tenths place of 85.935?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 7
Problem: What digit is in the tenths place of 83.414?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 4
Worked Example 8
Problem: What digit is in the tenths place of 24.788?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 7
Worked Example 9
Problem: What digit is in the tenths place of 22.561?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 5
Worked Example 10
Problem: What digit is in the tenths place of 14.971?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Practice Exercise
Create one new Grade 6 problem about Decimal tenths in expressions. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.2 Substituting decimal tenths
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What digit is in the tenths place of 53.135?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 1
Worked Example 2
Problem: What digit is in the tenths place of 65.176?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 1
Worked Example 3
Problem: What digit is in the tenths place of 21.925?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 4
Problem: What digit is in the tenths place of 66.823?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 8
Worked Example 5
Problem: What digit is in the tenths place of 10.898?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 8
Worked Example 6
Problem: What digit is in the tenths place of 44.253?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 7
Problem: What digit is in the tenths place of 54.255?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 8
Problem: What digit is in the tenths place of 76.966?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 9
Problem: What digit is in the tenths place of 11.304?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 10
Problem: What digit is in the tenths place of 18.266?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Practice Exercise
Create one new Grade 6 problem about Substituting decimal tenths. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.3 Adding decimal terms
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Calculate 88.967 + 14.085.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 103.052
Worked Example 2
Problem: Calculate 91.379 + 7.191.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 98.57
Worked Example 3
Problem: Calculate 95.294 + 1.715.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 97.009
Worked Example 4
Problem: Calculate 50.243 + 0.509.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 50.752
Worked Example 5
Problem: Calculate 24.998 + 5.087.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 30.085
Worked Example 6
Problem: Calculate 46.901 + 6.751.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 53.652
Worked Example 7
Problem: Calculate 41.378 + 12.284.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 53.662
Worked Example 8
Problem: Calculate 10.222 + 3.806.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 14.028
Worked Example 9
Problem: Calculate 23.118 + 16.45.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 39.568
Worked Example 10
Problem: Calculate 22.277 + 3.517.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 25.794
Practice Exercise
Create one new Grade 6 problem about Adding decimal terms. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.4 Subtracting decimal terms
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Calculate 32.584 - 12.299.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 20.285
Worked Example 2
Problem: Calculate 2.084 - 14.757.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: -12.673
Worked Example 3
Problem: Calculate 66.093 - 4.579.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 61.514
Worked Example 4
Problem: Calculate 6.102 - 2.144.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 3.958
Worked Example 5
Problem: Calculate 10.105 - 2.423.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 7.682
Worked Example 6
Problem: Calculate 24.843 - 15.331.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 9.512
Worked Example 7
Problem: Calculate 16.653 - 15.188.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 1.465
Worked Example 8
Problem: Calculate 87.82 - 2.999.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 84.821
Worked Example 9
Problem: Calculate 39.974 - 7.955.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 32.019
Worked Example 10
Problem: Calculate 27.238 - 5.958.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 21.28
Practice Exercise
Create one new Grade 6 problem about Subtracting decimal terms. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.5 Multiplying a variable by a decimal tenth
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Calculate 52.486 × 18.665.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 981.488
Worked Example 2
Problem: Calculate 8.596 × 8.714.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 74.785
Worked Example 3
Problem: Calculate 82.935 × 13.706.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 1136.209
Worked Example 4
Problem: Calculate 84.9 × 9.67.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 823.53
Worked Example 5
Problem: Calculate 43.368 × 14.636.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 633.173
Worked Example 6
Problem: Calculate 80.35 × 11.052.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 891.885
Worked Example 7
Problem: Calculate 80.538 × 8.509.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 684.573
Worked Example 8
Problem: Calculate 90.875 × 8.259.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 754.263
Worked Example 9
Problem: Calculate 86.125 × 7.16.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 620.1
Worked Example 10
Problem: Calculate 12.478 × 1.555.
- Line up or track place values carefully.
- Perform the operation.
- Estimate to check the result.
Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.
Answer: 19.965
Practice Exercise
Create one new Grade 6 problem about Multiplying a variable by a decimal tenth. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.6 Evaluating decimal expressions
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What digit is in the tenths place of 22.676?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 6
Worked Example 2
Problem: What digit is in the tenths place of 18.303?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 3
Problem: What digit is in the tenths place of 70.212?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 4
Problem: What digit is in the tenths place of 25.728?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 7
Worked Example 5
Problem: What digit is in the tenths place of 85.778?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 7
Worked Example 6
Problem: What digit is in the tenths place of 51.643?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 6
Worked Example 7
Problem: What digit is in the tenths place of 30.444?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 4
Worked Example 8
Problem: What digit is in the tenths place of 47.918?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 9
Problem: What digit is in the tenths place of 15.341?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 10
Problem: What digit is in the tenths place of 96.243?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Practice Exercise
Create one new Grade 6 problem about Evaluating decimal expressions. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.7 Money expressions
An algebraic expression combines numbers, variables, and operations without an equals sign. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Evaluate 3x + 4 when x = 5.
- Replace x with 5.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 19
Worked Example 2
Problem: Evaluate 2n + 7 when n = 6.
- Replace n with 6.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 19
Worked Example 3
Problem: Evaluate 5a - 3 when a = 4.
- Replace a with 4.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 17
Worked Example 4
Problem: Evaluate 4p + 1 when p = 8.
- Replace p with 8.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 33
Worked Example 5
Problem: Evaluate 6m - 5 when m = 3.
- Replace m with 3.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 13
Worked Example 6
Problem: Evaluate 2.5x + 1 when x = 4.
- Replace x with 4.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 11
Worked Example 7
Problem: Evaluate 7q + 2 when q = 2.
- Replace q with 2.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 16
Worked Example 8
Problem: Evaluate 3r - 1 when r = 9.
- Replace r with 9.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 26
Worked Example 9
Problem: Evaluate 4y + 6 when y = 5.
- Replace y with 5.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 26
Worked Example 10
Problem: Evaluate 8k - 4 when k = 3.
- Replace k with 3.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 20
Practice Exercise
Create one new Grade 6 problem about Money expressions. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
25.8 Measurement expressions
An algebraic expression combines numbers, variables, and operations without an equals sign. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Evaluate 3x + 4 when x = 5.
- Replace x with 5.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 19
Worked Example 2
Problem: Evaluate 2n + 7 when n = 6.
- Replace n with 6.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 19
Worked Example 3
Problem: Evaluate 5a - 3 when a = 4.
- Replace a with 4.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 17
Worked Example 4
Problem: Evaluate 4p + 1 when p = 8.
- Replace p with 8.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 33
Worked Example 5
Problem: Evaluate 6m - 5 when m = 3.
- Replace m with 3.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 13
Worked Example 6
Problem: Evaluate 2.5x + 1 when x = 4.
- Replace x with 4.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 11
Worked Example 7
Problem: Evaluate 7q + 2 when q = 2.
- Replace q with 2.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 16
Worked Example 8
Problem: Evaluate 3r - 1 when r = 9.
- Replace r with 9.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 26
Worked Example 9
Problem: Evaluate 4y + 6 when y = 5.
- Replace y with 5.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 26
Worked Example 10
Problem: Evaluate 8k - 4 when k = 3.
- Replace k with 3.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 20
Practice Exercise
Create one new Grade 6 problem about Measurement expressions. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
25.9 Tables with decimal outputs
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What digit is in the tenths place of 71.097?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 0
Worked Example 2
Problem: What digit is in the tenths place of 84.385?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 3
Problem: What digit is in the tenths place of 48.077?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 0
Worked Example 4
Problem: What digit is in the tenths place of 69.46?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 4
Worked Example 5
Problem: What digit is in the tenths place of 22.259?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 6
Problem: What digit is in the tenths place of 49.151?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 1
Worked Example 7
Problem: What digit is in the tenths place of 58.232?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 8
Problem: What digit is in the tenths place of 35.32?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 9
Problem: What digit is in the tenths place of 39.372?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 10
Problem: What digit is in the tenths place of 71.523?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 5
Practice Exercise
Create one new Grade 6 problem about Tables with decimal outputs. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.10 Estimating decimal expression values
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What digit is in the tenths place of 26.355?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 2
Problem: What digit is in the tenths place of 73.256?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 3
Problem: What digit is in the tenths place of 71.142?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 1
Worked Example 4
Problem: What digit is in the tenths place of 31.923?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 5
Problem: What digit is in the tenths place of 70.066?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 0
Worked Example 6
Problem: What digit is in the tenths place of 48.965?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 7
Problem: What digit is in the tenths place of 69.464?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 4
Worked Example 8
Problem: What digit is in the tenths place of 61.917?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 9
Problem: What digit is in the tenths place of 2.045?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 0
Worked Example 10
Problem: What digit is in the tenths place of 58.331?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Practice Exercise
Create one new Grade 6 problem about Estimating decimal expression values. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.11 Checking decimal calculations
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What digit is in the tenths place of 23.178?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 1
Worked Example 2
Problem: What digit is in the tenths place of 7.934?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 3
Problem: What digit is in the tenths place of 2.981?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 9
Worked Example 4
Problem: What digit is in the tenths place of 88.425?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 4
Worked Example 5
Problem: What digit is in the tenths place of 90.323?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 3
Worked Example 6
Problem: What digit is in the tenths place of 79.033?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 0
Worked Example 7
Problem: What digit is in the tenths place of 12.751?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 7
Worked Example 8
Problem: What digit is in the tenths place of 14.296?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 9
Problem: What digit is in the tenths place of 5.866?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 8
Worked Example 10
Problem: What digit is in the tenths place of 50.671?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 6
Practice Exercise
Create one new Grade 6 problem about Checking decimal calculations. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
25.12 Real-life decimal algebra
A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What digit is in the tenths place of 37.48?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 4
Worked Example 2
Problem: What digit is in the tenths place of 83.173?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 1
Worked Example 3
Problem: What digit is in the tenths place of 97.699?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 6
Worked Example 4
Problem: What digit is in the tenths place of 34.25?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 5
Problem: What digit is in the tenths place of 79.821?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 8
Worked Example 6
Problem: What digit is in the tenths place of 84.549?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 5
Worked Example 7
Problem: What digit is in the tenths place of 91.785?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 7
Worked Example 8
Problem: What digit is in the tenths place of 88.728?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 7
Worked Example 9
Problem: What digit is in the tenths place of 49.236?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 2
Worked Example 10
Problem: What digit is in the tenths place of 75.507?
- The first digit to the right of the decimal point is the tenths digit.
Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.
Answer: 5
Practice Exercise
Create one new Grade 6 problem about Real-life decimal algebra. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is lining up the last digits instead of lining up decimal points and place values.
30 Review Questions and Answers
Q1. What is important to understand about Decimal tenths in expressions?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q2. What is important to understand about Substituting decimal tenths?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q3. What is important to understand about Adding decimal terms?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q4. What is important to understand about Subtracting decimal terms?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q5. What is important to understand about Multiplying a variable by a decimal tenth?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q6. What is important to understand about Evaluating decimal expressions?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q7. What is important to understand about Money expressions?
Answer: An algebraic expression combines numbers, variables, and operations without an equals sign.
Q8. What is important to understand about Measurement expressions?
Answer: An algebraic expression combines numbers, variables, and operations without an equals sign.
Q9. What is important to understand about Tables with decimal outputs?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q10. What is important to understand about Estimating decimal expression values?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q11. What is important to understand about Checking decimal calculations?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
Q12. What is important to understand about Real-life decimal algebra?
Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.
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 help prevent incompatible quantities from being mixed.
Q16. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q17. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, a table, 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 and check copied values, operations, signs, units, rules, and calculations.
Q21. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q22. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q23. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q24. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q25. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q26. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q27. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q28. What is a good way to learn from a mistake?
Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.
Q29. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.
Q30. What does representing mathematics mean?
Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.