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.

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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:

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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 — by topic and difficulty, with answer keys.
• Math Topics Library — every conversion topic explained.
• Elementary Math eBooks — full workbooks.

Frequently Asked Questions

Why is \(\dfrac{1}{3}\) a repeating decimal?
Because \(1 \div 3\) does not terminate. \(\dfrac{1}{3} = 0.333\overline{3}\).

When should I round repeating decimals?
On most tests, leave the answer as a fraction or use the repeating-bar notation \(0.\overline{3}\). For real-world calculation, round to 2 or 3 decimal places.

Is 125% a real percent?
Yes — percents can be any value, including over 100%. 125% just means “more than the whole.”

What is a “percent of a percent”?
Multiply. 50% of 20% = \(0.50 \times 0.20 = 0.10 = 10\%\).

How do I convert a mixed number to a decimal?
Convert the fractional part separately. \(2\dfrac{3}{4} = 2 + 0.75 = 2.75\).

Should I memorize percent-to-fraction conversions?
At least the 12 in this guide. They show up on every test from 5th grade through the GRE.

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.

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