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
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
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
- The tenths place is the first digit to the right of the decimal point.
- In 4.73, that digit is 7.
Answer: 7
2. Decimals, Roots, and Real Numbers Checkpoint review from Decimal Place Value and Rounding: Write seven tenths as a decimal.
Show solution
- Tenths are one place to the right of the decimal.
- Seven tenths is 0.7.
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
- Write 0.9 as 0.900.
- 0.900 is greater than 0.870, 0.790, and 0.809.
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
- The tenths digit is 2.
- The hundredths digit is 8, so round 2 up to 3.
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
- The hundredths digit is 4.
- The thousandths digit is 6, so round 4 up to 5.
Answer: 12.75
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