Decimal to Fraction and Repeating Decimal Converter

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common decimals as fractions 0.25 0.125 0.375

Common decimals as fractions: 0.25, 0.5, 0.75, 0.125

The terminating decimals that show up most in real life are few, and every one has a short fraction. Below are the values from 0.05 to 0.875 and the rule that produces them, so you can check any other decimal in the tool.

The rule and the shortcuts to memorize

Every terminating decimal is a fraction with denominator 10, 100, 1000 and so on, depending on the number of places. 0.25 has two places and equals 25/100; the gcd of 25 and 100 is 25, so the fraction in lowest terms is 1/4. 0.125 has three places, equals 125/1000 and the gcd is 125, which gives 1/8. The final denominator can only contain the factors 2 and 5, because it comes from dividing a power of 10, which is why fractions of terminating decimals have denominators like 2, 4, 5, 8, 10, 16, 20, 25, 40 and 50, and never 3, 6, 7 or 9.
The tenths follow the five times table: 0.2 = 1/5, 0.4 = 2/5, 0.6 = 3/5 and 0.8 = 4/5, while 0.5 = 1/2. The quarters are 0.25 = 1/4, 0.5 = 2/4 and 0.75 = 3/4. The eighths come from halving 0.25: 0.125 = 1/8, 0.375 = 3/8, 0.625 = 5/8 and 0.875 = 7/8, each 0.125 larger than the one before. With two places you get 0.05 = 1/20, 0.04 = 1/25, 0.02 = 1/50 and 0.01 = 1/100, which match 5%, 4%, 2% and 1%.
In practice these values show up in inches and recipes (3/8 inch is 0.375 and 1/8 cup is 0.125), in discounts (0.15 is 3/20) and in probabilities. A shortcut for reducing by hand: if the decimal ends in 25 or 75, divide by 25; if it ends in 5, divide by 5; if it is even, keep dividing by 2. To check, divide the numerator by the denominator: 7 ÷ 8 = 0.875.

Checked examples

One quarter

Input: 0,25
Expected output: 1/4

25/100 divided by 25.

Three quarters

Input: 0,75
Expected output: 3/4

75/100 divided by 25.

One eighth

Input: 0,125
Expected output: 1/8

125/1000 divided by 125.

Three eighths

Input: 0,375
Expected output: 3/8

375/1000 divided by 125.

Seven eighths

Input: 0,875
Expected output: 7/8

875/1000 divided by 125.

Five percent

Input: 0,05
Expected output: 1/20

5/100 divided by 5.

Three fifths

Input: 0,6
Expected output: 3/5

6/10 divided by 2.

Full tool FAQ

How do you turn a decimal into a fraction?

Count the decimal places, write the digits without the point as the numerator and use 1 followed by that many zeros as the denominator. Then reduce by the gcd. Example: 0.375 has 3 places, becomes 375/1000 and, dividing by 125, 3/8. With an integer part, 2.5 = 25/10 = 5/2 = 2 1/2.

What is the fraction of a repeating decimal?

How do you convert a purely repeating decimal?

What about a repeating decimal with non-repeating digits first?

Is 0.999... really equal to 1?

How can I tell if a fraction terminates or repeats?

How do I type a repeating decimal?

Does it handle negatives, percentages and mixed numbers?

Why do π and √2 have no fraction?

Is there a size limit?

Frequently asked questions

What is the fraction for 0.5?

1/2. The decimal 0.5 has one place, becomes 5/10 and the gcd is 5. It is the only one-place decimal whose fraction has denominator 2; the others have 5 (0.2 = 1/5) or 10 (0.1 = 1/10, 0.3 = 3/10).

How do I convert 0.333 to a fraction?

Because 0.333 ends, it equals 333/1000, which is already in lowest terms and is not 1/3. Only 0.333... with a repeating block (0.(3)) equals 1/3. The gap is 1/3000, small but real, which is why the repeating-block notation matters.

Why is 0.2 written 1/5 and not 2/10?

The two fractions are equal, but 2/10 can still be divided by 2. The lowest-terms form, where numerator and denominator share no factor, is 1/5, and it is the one tests ask for.

What about decimals with an integer part, like 2.75?

Treat the whole number: 2.75 = 275/100 = 11/4, which is also written 2 3/4 as a mixed number. Another way is to keep the 2 and convert only 0.75 to 3/4.

Next steps

Decimal	Fraction
0,25	1/4
0,(3)	1/3
1,2(5)	113/90
-0,8	-4/5

Decimal

Fraction

0,25

1/4

0,(3)

1/3

1,2(5)

113/90

-0,8

-4/5

The rule and the shortcuts to memorize

Every terminating decimal is a fraction with denominator 10, 100, 1000 and so on, depending on the number of places. 0.25 has two places and equals 25/100; the gcd of 25 and 100 is 25, so the fraction in lowest terms is 1/4. 0.125 has three places, equals 125/1000 and the gcd is 125, which gives 1/8. The final denominator can only contain the factors 2 and 5, because it comes from dividing a power of 10, which is why fractions of terminating decimals have denominators like 2, 4, 5, 8, 10, 16, 20, 25, 40 and 50, and never 3, 6, 7 or 9.

The tenths follow the five times table: 0.2 = 1/5, 0.4 = 2/5, 0.6 = 3/5 and 0.8 = 4/5, while 0.5 = 1/2. The quarters are 0.25 = 1/4, 0.5 = 2/4 and 0.75 = 3/4. The eighths come from halving 0.25: 0.125 = 1/8, 0.375 = 3/8, 0.625 = 5/8 and 0.875 = 7/8, each 0.125 larger than the one before. With two places you get 0.05 = 1/20, 0.04 = 1/25, 0.02 = 1/50 and 0.01 = 1/100, which match 5%, 4%, 2% and 1%.

In practice these values show up in inches and recipes (3/8 inch is 0.375 and 1/8 cup is 0.125), in discounts (0.15 is 3/20) and in probabilities. A shortcut for reducing by hand: if the decimal ends in 25 or 75, divide by 25; if it ends in 5, divide by 5; if it is even, keep dividing by 2. To check, divide the numerator by the denominator: 7 ÷ 8 = 0.875.

Checked examples

One quarter

Input: 0,25
Expected output: 1/4

25/100 divided by 25.

Three quarters

Input: 0,75
Expected output: 3/4

75/100 divided by 25.

One eighth

Input: 0,125
Expected output: 1/8

125/1000 divided by 125.

Three eighths

Input: 0,375
Expected output: 3/8

375/1000 divided by 125.

Seven eighths

Input: 0,875
Expected output: 7/8

875/1000 divided by 125.

Five percent

Input: 0,05
Expected output: 1/20

5/100 divided by 5.

Three fifths

Input: 0,6
Expected output: 3/5

6/10 divided by 2.

Full tool FAQ

How do you turn a decimal into a fraction?

What is the fraction of a repeating decimal?

How do you convert a purely repeating decimal?

What about a repeating decimal with non-repeating digits first?

Is 0.999... really equal to 1?

How can I tell if a fraction terminates or repeats?

How do I type a repeating decimal?

Does it handle negatives, percentages and mixed numbers?

Why do π and √2 have no fraction?

Is there a size limit?

Frequently asked questions

What is the fraction for 0.5?

1/2. The decimal 0.5 has one place, becomes 5/10 and the gcd is 5. It is the only one-place decimal whose fraction has denominator 2; the others have 5 (0.2 = 1/5) or 10 (0.1 = 1/10, 0.3 = 3/10).

How do I convert 0.333 to a fraction?

Why is 0.2 written 1/5 and not 2/10?

The two fractions are equal, but 2/10 can still be divided by 2. The lowest-terms form, where numerator and denominator share no factor, is 1/5, and it is the one tests ask for.

What about decimals with an integer part, like 2.75?

Treat the whole number: 2.75 = 275/100 = 11/4, which is also written 2 3/4 as a mixed number. Another way is to keep the 2 and convert only 0.75 to 3/4.