Fractions, Decimals, and Percents: Conversion Guide

Fractions, decimals, and percents are three names for the same idea. \(\dfrac{1}{2}\), $0.5$, and \(50\%\) all describe “half.” Once your brain accepts this, every test from 5th grade to the GRE gets easier, because you can pick the form that solves the problem fastest.

This guide gives you every conversion rule, worked examples, and the common conversions you should know cold.

The Big Idea

A fraction is a part of a whole written as \(\dfrac{a}{b}\). A decimal is a part of a whole written using place value: $0.5$, $0.25$, $0.125$. A percent is a fraction with a denominator of 100: \(50\% = \dfrac{50}{100}\).

They are interchangeable. Conversion is just translation.

The 6 Conversion Rules

Rule 1: Fraction → Decimal

Divide the numerator by the denominator.

\[\dfrac{3}{4} = 3 \div 4 = 0.75\]

\[\dfrac{1}{8} = 1 \div 8 = 0.125\]

If the division terminates, you get a clean decimal. If not, you get a repeating decimal: \(\dfrac{1}{3} = 0.3333\ldots = 0.\overline{3}\).

Rule 2: Decimal → Fraction

Place the decimal over the appropriate power of 10, then simplify.

\(0.75 = \dfrac{75}{100} = \dfrac{3}{4}\) (dividing top and bottom by 25)

\(0.6 = \dfrac{6}{10} = \dfrac{3}{5}\)

\(0.125 = \dfrac{125}{1000} = \dfrac{1}{8}\)

Rule 3: Decimal → Percent

Multiply by 100 (or move the decimal point two places to the right).

\(0.75 \rightarrow 75\%\)

\(0.06 \rightarrow 6\%\)

\(1.25 \rightarrow 125\%\)

Rule 4: Percent → Decimal

Divide by 100 (or move the decimal point two places to the left).

\(60\% \rightarrow 0.60\)

\(3\% \rightarrow 0.03\)

\(125\% \rightarrow 1.25\)

Rule 5: Fraction → Percent

Either convert to a decimal first and then multiply by 100, or rewrite the fraction with a denominator of 100.

\(\dfrac{3}{4} = 0.75 = 75\%\)

\(\dfrac{2}{5} = \dfrac{40}{100} = 40\%\)

Rule 6: Percent → Fraction

Put the percent over 100 and simplify.

\(75\% = \dfrac{75}{100} = \dfrac{3}{4}\)

\(20\% = \dfrac{20}{100} = \dfrac{1}{5}\)

\(12.5\% = \dfrac{12.5}{100} = \dfrac{125}{1000} = \dfrac{1}{8}\)

The 12 Conversions to Memorize

If you memorize these, you will solve 80% of conversion problems instantly:

Print this table. Stick it on the wall. Reread it every day for a week. They become permanent.

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Worked Examples by Difficulty

Easy

Convert 0.4 to a fraction. \(0.4 = \dfrac{4}{10} = \dfrac{2}{5}\).

Medium

Convert \(\dfrac{7}{20}\) to a percent. Multiply top and bottom by 5: \(\dfrac{35}{100} = 35\%\).

Or: \(7 \div 20 = 0.35 = 35\%\).

Harder

Express 0.125 as a percent and as a fraction. – As a percent: \(0.125 \times 100 = 12.5\%\). – As a fraction: \(\dfrac{125}{1000} = \dfrac{1}{8}\).

Hardest (test-prep level)

A shirt is marked 20% off. Its sale price is \$32. What was the original price?

20% off means the customer pays 80% of the original. Let \(x\) = original price.

\(0.80x = 32\)

\(x = \dfrac{32}{0.80} = 40\).

Original price: \$40.

Common Mistakes

Confusing percent and decimal

\(6\% = 0.06\), not $0.6$. Move the decimal two places.

Forgetting to simplify

\(0.4 = \dfrac{4}{10}\), but the simplified answer is \(\dfrac{2}{5}\). Most tests want the simplest form.

Misplacing the decimal point

\(\dfrac{1}{8} = 0.125\), not $0.0125$ or $1.25$. Long division catches this.

Confusing 12.5% with \(\dfrac{1}{12}\)

\(\dfrac{1}{12} \approx 0.0833 = 8.33\%\), not 12.5%. Don’t guess.

Treating “of” wrong

“30% of 40″ means \(0.30 \times 40 = 12\), not 30% + 40.

How to Practice

1. Daily conversion warm-up. Five conversions every day for 2 weeks. By day 14, the patterns are automatic.
2. Flashcards with the 12 must-know conversions on each card.
3. Real-world practice, every time you see a percent (tax, tip, discount), convert it to a fraction in your head.
4. Free worksheets, print and practice.
5. A wall chart of the 12 must-know conversions.

Free Resources

Effortless Math has a complete free conversion library:

• Fractions, Decimals, Percents Worksheets (resource currently unavailable), by topic and difficulty, with answer keys.
• Math Topics Library, every conversion topic explained.
• Elementary Math eBooks, full workbooks.

Frequently Asked Questions

How do you convert fractions to decimals to percents? Divide the numerator by the denominator to get the decimal, then multiply by 100 and add a percent sign. For 3/8, 3 ÷ 8 = 0.375, and 0.375 × 100 = 37.5%. For 5/8, 5 ÷ 8 = 0.625, or 62.5%. If the denominator is easy to scale to 100, you can skip the division: 3/4 = 75/100 = 0.75 = 75%.

How do you convert a decimal to a fraction? Use place value. Write the digits after the decimal point over 10, 100 or 1,000, depending on how many decimal places there are, then simplify. For 0.62, write 62/100 and simplify to 31/50. For 0.375, write 375/1000, which simplifies to 3/8. Repeating decimals need a different method, but it helps to memorize that 0.333… equals 1/3.

Are fractions decimals? Fractions and decimals are two ways of writing the same value. The fraction 1/2, the decimal 0.5 and the percent 50% all mean one half. Every fraction can be written as a decimal that either terminates, like 1/4 = 0.25, or repeats, like 1/3 = 0.333…, and both kinds are rational numbers. Pick whichever form makes a problem easier to solve.

Is there a fractions, decimals and percents conversion chart? Yes. A conversion chart lists common values in all three forms, and memorizing them saves time on tests. Key ones include 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/8 = 0.125 = 12.5%, 1/10 = 0.1 = 10% and 1/3 ≈ 0.333, or about 33.3%. Making your own chart is good practice in itself.

How do you convert percents to decimals and fractions? To change a percent to a decimal, divide by 100 by moving the decimal point two places to the left: 45% = 0.45. To make it a fraction, write the percent over 100 and simplify: 45% = 45/100 = 9/20. A percent with a decimal works the same way: 12.5% = 0.125 = 125/1000 = 1/8.

You’re Three Steps From Fluency

Conversion fluency comes from repetition with a small set of values. Memorize the 12 in the table. Practice the rules until they’re automatic. Watch your test scores rise across every topic that touches fractions, decimals, or percents, which is most of them.

Keep Practicing With the Right Resources