Decimal Place Value and Rounding
A free Pre-Algebra lesson from the “Decimals, Roots, and the Real Number System” unit, with a worked example and practice problems including step-by-step solutions.
Decimals extend the place-value system to numbers smaller than one. The first place to the right of the decimal is tenths, then hundredths, then thousandths. To compare decimals, line up the decimal points and compare from left to right.
What you'll learn
- Read decimal place values
- Compare and order decimals
- Round decimals to a given place
Worked example
Problem. Round 14.268 to the nearest hundredth.
- The hundredths digit is 6.
- Look at the thousandths digit, which is 8.
- Since 8 is 5 or greater, round the hundredths digit up to get 14.27.
Answer: 14.27
Practice problems
1. What digit is in the tenths place of 4.73?
Show solution
- Warm-up: First identify exactly what the question is asking: What digit is in the tenths place of 4.73?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- The tenths place is the first digit to the right of the decimal point.
- In 4.73, that digit is 7.
- Check the result by substituting or estimating: the response should match 7 and make sense in the original problem.
Answer: 7
2. Write seven tenths as a decimal.
Show solution
- Warm-up: First identify exactly what the question is asking: Write seven tenths as a decimal.
- For decimals, keep place value aligned and use estimation to make sure the decimal point is reasonable.
- Tenths are one place to the right of the decimal.
- Seven tenths is 0.7.
- Check the result by substituting or estimating: the response should match 0.7 and make sense in the original problem.
Answer: 0.7
3. Which number is greatest?
Choices: 0.87 · 0.9 · 0.79 · 0.809
Show solution
- Warm-up: First identify exactly what the question is asking: Which number is greatest?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Write 0.9 as 0.900.
- 0.900 is greater than 0.870, 0.790, and 0.809.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: 0.9
4. Round 6.284 to the nearest tenth.
Show solution
- Core Practice: First identify exactly what the question is asking: Round 6.284 to the nearest tenth.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- The tenths digit is 2.
- The hundredths digit is 8, so round 2 up to 3.
- Check the result by substituting or estimating: the response should match 6.3 and make sense in the original problem.
Answer: 6.3
5. Round 12.746 to the nearest hundredth.
Show solution
- Core Practice: First identify exactly what the question is asking: Round 12.746 to the nearest hundredth.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- The hundredths digit is 4.
- The thousandths digit is 6, so round 4 up to 5.
- Check the result by substituting or estimating: the response should match 12.75 and make sense in the original problem.
Answer: 12.75
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