Decimal, Fraction, and Percent Conversions
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, fractions, and percents are different ways to write the same value. Percent means per 100. Fractions can become decimals by dividing, and decimals can become percents by multiplying by 100.
What you'll learn
- Convert decimals to fractions and percents
- Convert fractions to decimals and percents
- Use benchmark conversions fluently
Why it matters: A 25% off tag, a 1/4 measuring cup, and a 0.25 meter reading are the same value in three forms. Conversion fluency is how prices, recipes, and labels stay readable across contexts.
Worked example
Problem. Write 0.375 as a percent and a fraction.
- Multiply 0.375 by 100 to get 37.5%.
- 0.375 = 375/1000.
- Simplify 375/1000 to 3/8.
Answer: 37.5% and 3/8
Practice problems
1. Write 0.6 as a percent.
Show solution
- Warm-up: First identify exactly what the question is asking: Write 0.6 as a percent.
- For percents, convert the percent to a decimal or fraction and connect it to the base amount in the problem.
- Multiply 0.6 by 100.
- 0.6 = 60%.
- Check the result by substituting or estimating: the response should match 60 and make sense in the original problem.
Answer: 60
2. Write 35% as a decimal.
Show solution
- Warm-up: First identify exactly what the question is asking: Write 35% as a decimal.
- For decimals, keep place value aligned and use estimation to make sure the decimal point is reasonable.
- Divide 35 by 100.
- 35% = 0.35.
- Check the result by substituting or estimating: the response should match 0.35 and make sense in the original problem.
Answer: 0.35
3. Write 1/4 as a decimal.
Show solution
- Warm-up: First identify exactly what the question is asking: Write 1/4 as a decimal.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- 1 divided by 4 is 0.25.
- So 1/4 = 0.25.
- Check the result by substituting or estimating: the response should match 0.25 and make sense in the original problem.
Answer: 0.25
4. Write 3/5 as a percent.
Show solution
- Core Practice: First identify exactly what the question is asking: Write 3/5 as a percent.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- 3 divided by 5 is 0.6.
- 0.6 = 60%.
- Check the result by substituting or estimating: the response should match 60 and make sense in the original problem.
Answer: 60
5. Write 0.125 as a fraction in simplest form.
Show solution
- Core Practice: First identify exactly what the question is asking: Write 0.125 as a fraction in simplest form.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- 0.125 = 125/1000.
- 125/1000 simplifies to 1/8.
- Check the result by substituting or estimating: the response should match 1/8 and make sense in the original problem.
Answer: 1/8
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