Math · Numbers, fractions & decimals
Fractions, Decimals, and Percents
Estimated study time. Take the time you need.
Start here: key ideas
- Fraction to decimal means numerator divided by denominator.
- Decimal to percent moves the decimal two places right.
- Percent to decimal moves it two places left.
- Write percent over 100, then simplify.
What you’ll be able to do
- Convert among fractions, decimals, and percents.
- Recall benchmark equivalents.
- Choose a useful representation for comparison.
Treat fraction, decimal, and percent as three names for one quantity.
Review fraction simplification and decimal place value first.
One amount, three names
A percent is a ratio per hundred. The statements 3/4, 0.75, and 75% are equivalent: they name the same point on the number line. A benchmark is a familiar equivalent used for quick comparison: 1/2=0.5=50%, 1/4=0.25=25%, and 3/4=0.75=75%.
Denny Burzynski and Wade Ellis, Jr. / OpenStax CNX, via Mathematics LibreTexts · CC BY · https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/07%3A_Ratios_and_Rates/7.04%3A_Percent · https://creativecommons.org/licenses/by/ · Source image reproduced unchanged.
Convert in every direction
To change a fraction to a decimal, divide numerator by denominator. A terminating decimal ends, as 3/8=0.375. A repeating decimal continues a pattern, as 2/3=0.666…. To change a decimal to a percent, multiply by 100 and write %. Thus 0.42=42%. To change a percent to a decimal, divide by 100: 7%=0.07.
To make a fraction from a decimal, read its place value: 0.36=36/100=9/25. To make a fraction from a percent, place it over 100 and simplify: 35%=35/100=7/20. A percent can exceed 100%; 125%=1.25=5/4.
Choose the easiest form
Convert all values to the same form before comparing. For 5/8 and 60%, either compute 5÷8=0.625 and compare with 0.60, or recognize 60%=3/5. Keep exact values until the end; early rounding can reverse close comparisons.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/2 | 0.50 | 50% |
| 3/4 | 0.75 | 75% |
Worked examples
Worked example 1: Convert 7/20. Divide 7÷20=0.35; multiply by 100 to obtain 35%.
Worked example 2: Order 0.58, 3/5, and 57%. Convert to decimals: 0.58, 0.60, 0.57. Therefore 57%<0.58<3/5.
A reliable way to reason
Conversion changes notation, not quantity. Picture one point on a number line wearing three labels. This prevents a common error: believing 0.4, 4%, and 4/10 are equivalent. In fact, 0.4=40%=4/10, while 4%=0.04=1/25. The percent sign supplies a hidden division by 100.
Use the form that exposes the comparison. To compare 7/12 and 58%, convert 7/12 to about 0.5833 and 58% to 0.58; the fraction is slightly larger. To calculate 25% of a quantity, the fraction 1/4 may be fastest. To show part of 100, percent is clearest. For a repeating result, preserve exactness when possible: 2/3 is exact, while 0.67 is a rounded approximation. If rounding is required, convert first, then round at the requested place. A final benchmark check protects scale: values below 1 correspond to percents below 100%; values above 1 correspond to percents above 100%. Thus 1.08 must be 108%, not 10.8%.
Guided reasoning and error checks
Check a conversion by reversing it: 62.5%=5/8 because 5÷8=0.625. For close values, carry enough digits. Comparing 5/6 with 83% requires 0.8333… versus 0.83; rounding too early would hide that the fraction is larger. Exact fractions are often the safest intermediate form.
Final self-check
Before finalizing a conversion, ask whether the scale is believable. A positive fraction smaller than 1 must become a decimal between 0 and 1 and a percent between 0% and 100%. For example, 11/20 becomes 0.55 and 55%. If a computation produced 5.5% or 550%, the digits may look familiar, but the scale test proves the decimal moved the wrong number of places.
Key terms
- percent: A ratio measured per hundred.
- benchmark: A familiar value used for comparison.
- equivalent: Equal in value despite a different form.
- terminating decimal: A decimal with finitely many digits.
- repeating decimal: A decimal with a recurring digit pattern.
Summary
- Use division for fraction-to-decimal conversion.
- Attach or remove the percent scale by factors of 100.
- Convert all quantities to one form before comparing.
- Benchmark equivalents such as 1/2 = 0.5 = 50% make conversions and comparisons easier to check.
Percent means “out of 100”: decimal ×100 gives percent; percent ÷100 gives decimal.
Sources
Lesson checks
Reading is free. Starting checks uses your existing free-topic activity allowance; other assessment access rules still apply.
Reading on this device
This reading marker stays in this browser. It is not a saved account quiz result or mastery evidence.
Save your reading place
Reading progress is separate from quiz performance.
Create an account to save your reading or sign in. All lesson text stays available without signing in.More practice
Practice has its own access rules. It does not change access to this lesson.
See practice options