Converting Terminating Decimals

Put the decimal over 1, multiply both numbers by 10 for every digit after the decimal point, then reduce:

0.75
= 75/100 (2 decimal places → multiply by 100)
= 3/4 (divide by GCF of 25)
= ¾
0.625
= 625/1000 (3 decimal places)
= 5/8 (divide by GCF of 125)
= ⅝
0.4
= 4/10 (1 decimal place)
= 2/5
= 2/5

Decimal Place Reference

Decimal placesDenominator to use
1 (e.g. 0.3)10
2 (e.g. 0.25)100
3 (e.g. 0.125)1000
4 (e.g. 0.0625)10,000

Converting Mixed Decimal Numbers

When the number is bigger than 1, like 2.35, split off the whole part and convert just the decimal part on its own:

2.35
Whole part: 2
Decimal part: 0.35 = 35/100 = 7/20
Result: 2 7/20

Converting Repeating Decimals

Decimals that repeat forever, like 0.333... or 0.142857142857..., need a bit of algebra instead of simple multiplication:

Convert 0.333... to a fraction:
Let x = 0.333...
10x = 3.333...
10x − x = 3.333... − 0.333...
9x = 3
x = 3/9 = 1/3
Convert 0.272727... to a fraction:
Let x = 0.272727...
100x = 27.272727...
100x − x = 27
99x = 27
x = 27/99 = 3/11

Common Decimal-Fraction Pairs

DecimalFraction
0.51/2
0.251/4
0.753/4
0.11/10
0.21/5
0.333...1/3
0.666...2/3
0.1251/8
0.3753/8
0.6255/8

Using the Fraction Calculator

The SolverCalc fraction calculator handles decimals and fractions together in either direction. Want to check it by hand instead? Divide the fraction back out on the scientific calculator and confirm it lands on your original decimal.