Math · Decimals

Converting Between Fractions and Decimals

Fractions and decimals are two ways of writing the exact same amount. Once you can move between them, you can pick whichever form is easiest for the problem in front of you.

Part 01

Decimals to Fractions

The number of decimal places tells you exactly what denominator to use: 1 place means tenths (over 10), 2 places means hundredths (over 100). Write the digits (without the point) as the numerator, then simplify.

Decimal0.6
610
35

0.6 has 1 decimal place, so it's 6 tenths: 6/10. Both 6 and 10 can be divided by their greatest common factor, 2, giving the simplified fraction 3/5.

Decimal0.75
75100
34

0.75 has 2 decimal places, so it's 75 hundredths: 75/100. The greatest common factor of 75 and 100 is 25, giving 3/4.

Don't forget the last step ✅

Writing the fraction is only half the job — always check whether it can be simplified. A fraction is fully simplified when the numerator and denominator share no common factor besides 1.

Part 02

Fractions to Decimals

There are two ways to turn a fraction into a decimal. Use whichever one fits the problem:

1

Build an equivalent power-of-10 fraction

If the denominator is a factor of 10, 100, or 1000, multiply the top and bottom by the same number to reach a power of 10 — then write it straight as a decimal.

2

Divide the numerator by the denominator

This always works, for any fraction — a fraction bar just means division. Use long division, adding a decimal point and zeros to the numerator as needed.

Method 1 — 4 is a factor of 100, so multiply top and bottom by 25:

34
×
2525
=
75100
Decimal0.75

Method 2 — 8 isn't a factor of 10, 100, or 1000, so divide instead. Since 1 doesn't divide evenly by 8, add a decimal point and zeros to keep going: 1 becomes 1.000.

18
Add zeros1.000 ÷ 8
1/8 = 1.000 ÷ 8 = 0.125

Heads up — some decimals never end 🔁

Try dividing 1 by 3: 1.000 ÷ 3 = 0.333, and it keeps going forever — 0.3333... This is called a repeating decimal. We won't practice those here, but it's good to know they exist!

Your Turn!

Practice

Work through each conversion in two stages.

Practice — Decimal to Fraction

Convert to a simplified fraction

Stage 1 — Write the unsimplified fraction
Stage 2 — Simplify
Practice — Fraction to Decimal

Convert to a decimal

Here's the fraction.

Stage 1 — Find the multiplier
Stage 2 — Write the decimal