Decimals, Roots, and Real Numbers Checkpoint
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.
This checkpoint mixes the decimals, roots, and the real number system skills from the unit. It is intentionally cumulative: students identify the topic, choose a method, solve, and check that the answer makes sense before moving on. In Decimals, Roots, and the Real Number System, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Review the major skills from Decimals, Roots, and the Real Number System
- Choose methods without topic labels
- Explain and check work across a mixed set
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.
- Connect the calculation back to Decimal Place Value and Rounding so the method, not just the arithmetic, is clear.
Answer: 14.27
Practice problems
1. Decimals, Roots, and Real Numbers Checkpoint review from Decimal Place Value and Rounding: 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. Decimals, Roots, and Real Numbers Checkpoint review from Decimal Place Value and Rounding: 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. Decimals, Roots, and Real Numbers Checkpoint review from Decimal Place Value and Rounding: 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. Decimals, Roots, and Real Numbers Checkpoint review from Decimal Place Value and Rounding: 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. Decimals, Roots, and Real Numbers Checkpoint review from Decimal Place Value and Rounding: 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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