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Master Decimal to Fraction

Convert a decimal to a simplified fraction. For example, 0.75 = 3/4. Use place value or a denominator that is a power of 10, then reduce to lowest terms.

What is Decimal to Fraction Conversion?

Writing decimals as fractions in lowest terms

To convert a decimal to a fraction, use place value: the digits after the decimal point tell you the denominator (e.g. two digits → hundredths). Write as a fraction over a power of 10, then reduce to lowest terms. Example: 0.75 = 75/100 = 3/4.

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Place Value

Use place value to get a fraction over 10, 100, 1000, etc., then simplify.

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Decimal to Fraction Rules

Key steps for converting decimals to fractions

Terminating Decimals

Count decimal places. Denominator = 10^n (e.g. 2 places → 100). Numerator = the number without the decimal point. Then simplify.

0.75 = \frac{75}{100} = \frac{3}{4}
0.4 = \frac{4}{10} = \frac{2}{5}

Simplify to Lowest Terms

Divide numerator and denominator by their GCD to get the fraction in lowest terms.

0.125 = \frac{125}{1000} = \frac{1}{8}

Decimal to Fraction Examples

Worked examples

Basic Examples

0.75\frac{3}{4}
0.4\frac{2}{5}
0.125\frac{1}{8}

Why Decimal to Fraction Matters

Converting decimals to fractions helps with exact arithmetic and comparing sizes. Many problems are easier in fraction form.

Applications

Used in measurements, probability, and whenever exact rational form is needed.

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Decimal to Fraction Practice

Practice converting decimals to simplified fractions with easy, medium, and hard levels.

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