Curriculum›4B›Chapter 12

Rounding Decimals

Semester 4B · Chapter 12 · Lesson 8 · MATH-4B-C12-L08

Learning goal: Round decimals to a named precision with midpoint reasoning.

Before you begin: prerequisite check

Recall: 4A rounding whole numbers; 12.08. Attempt these questions independently first.

Question 1 · comparison

Insert <, > or =: 0.40 ___ 0.77.

Show answer and reasoning
<

Compare 40 hundredths and 77 hundredths; 0.40 is less relative to 0.77.

Question 2 · comparison

Insert <, > or =: 0.79 ___ 0.52.

Show answer and reasoning
>

Compare 79 hundredths and 52 hundredths; 0.79 is greater relative to 0.52.

Question 3 · comparison

Insert <, > or =: 0.51 ___ 0.64.

Show answer and reasoning
<

Compare 51 hundredths and 64 hundredths; 0.51 is less relative to 0.64.

Key vocabulary

tenth
one of ten equal parts of a whole
hundredth
one of one hundred equal parts
equivalent decimals
two notations for the same amount
midpoint
exact halfway point between rounding benchmarks

Understand the concept

Rounding replaces a number with a nearby value at a named place. To round 4.67 to the nearest tenth, compare 4.6 and 4.7; the midpoint is 4.65, so 4.67 rounds to 4.7. To round to the nearest whole, compare 4 and 5 instead. Always start with the original number rather than repeatedly rounding it to several places: double rounding can produce a different answer. Use the midpoint and the actual distance to justify a result.

Common misunderstanding to avoid: Repeated rounding rather than rounding original value

Fully worked examples and immediate checks

Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.

Worked example 1

Question 1 · rounding

Round 2.93 to the nearest whole number.

Answer: 3

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 2.93 directly.

Check 1: try it yourself

Question 1 · rounding

Round 8.57 to the nearest tenth.

Show answer and reasoning
8.6

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 8.57 directly.

Worked example 2

Question 2 · rounding

Round 8.99 to the nearest tenth.

Answer: 9.0

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 8.99 directly.

Check 2: try it yourself

Question 2 · rounding

Round 1.46 to the nearest whole number.

Show answer and reasoning
1

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 1.46 directly.

Worked example 3

Question 3 · rounding

Round 5.68 to the nearest whole number.

Answer: 6

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 5.68 directly.

Check 3: try it yourself

Question 3 · rounding

Round 9.21 to the nearest whole number.

Show answer and reasoning
9

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 9.21 directly.

Guided practice

Question 1 · rounding

Round 5.94 to the nearest whole number.

Show answer and reasoning
6

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 5.94 directly.

Question 2 · rounding

Round 6.31 to the nearest tenth.

Show answer and reasoning
6.3

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 6.31 directly.

Question 3 · rounding

Round 7.88 to the nearest whole number.

Show answer and reasoning
8

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 7.88 directly.

Question 4 · rounding

Round 2.71 to the nearest whole number.

Show answer and reasoning
3

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 2.71 directly.

Question 5 · rounding

Round 7.36 to the nearest whole number.

Show answer and reasoning
7

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 7.36 directly.

Independent practice

Question 1 · rounding

Round 9.43 to the nearest tenth.

Show answer and reasoning
9.4

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 9.43 directly.

Question 2 · rounding

Round 4.55 to the nearest tenth.

Show answer and reasoning
4.6

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 4.55 directly.

Question 3 · rounding

Round 1.40 to the nearest tenth.

Show answer and reasoning
1.4

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 1.40 directly.

Question 4 · rounding

Round 8.07 to the nearest whole number.

Show answer and reasoning
8

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 8.07 directly.

Question 5 · rounding

Round 3.43 to the nearest tenth.

Show answer and reasoning
3.4

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 3.43 directly.

Question 6 · rounding

Round 8.85 to the nearest whole number.

Show answer and reasoning
9

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 8.85 directly.

Question 7 · rounding

Round 2.54 to the nearest tenth.

Show answer and reasoning
2.5

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 2.54 directly.

Question 8 · rounding

Round 1.24 to the nearest tenth.

Show answer and reasoning
1.2

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 1.24 directly.

Challenge and transfer

Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.

Question 1 · reasoning

Round 5.98 to the nearest tenth. Explain how place value or a model can check your result.

Show answer and reasoning
6.0

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 5.98 directly. A correct explanation should name the relevant fractional place values and verify the answer.

Question 2 · error analysis

A learner claims: “To round 3.45 to the nearest whole, first round to 3.5 and then to 4.” Identify what is wrong or incomplete and give a mathematically correct explanation.

Show answer and reasoning
False: round the original 3.45 directly to the nearest whole: 3, not 4.

False: round the original 3.45 directly to the nearest whole: 3, not 4. Explain the relevant quantities or properties, not merely the final answer.

Exit check

Question 1 · rounding

Round 3.80 to the nearest tenth.

Show answer and reasoning
3.8

Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 3.80 directly.

Question 2 · rounding

Round 6.17 to the nearest whole number.

Show answer and reasoning
6

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 6.17 directly.

Question 3 · rounding

Round 8.32 to the nearest whole number.

Show answer and reasoning
8

Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 8.32 directly.

Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.

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