Decimal to Fraction Converter

Type a decimal to get the exact fraction in lowest terms, the mixed number, the working and the nearest ruler fraction down to 1/64.

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0.625 as a fraction

Fraction: 5/8; exact, in lowest terms
Mixed number: 5/8; less than 1, so no whole part
Before simplifying: 625/1000; divided top and bottom by 125
Nearest 1/16: 5/8; exact, no rounding needed
Percent: 62.5%; exact

Working, step by step

Step	What to do	Working
1	Count the decimal places	0.625 has 3 decimal places, so the denominator is 1 followed by 3 zeros: 1000
2	Write the digits over that denominator	0.625 = 625/1000
3	Simplify by the greatest common divisor	GCD(625, 1000) = 125, so 625/1000 = 5/8

Nearest ruler fractions

Rounded to the nearest	Fraction	Decimal value	Difference
1/2	1/2	0.5	0.125 too small
1/4	3/4	0.75	0.125 too big
1/8	5/8	0.625	exact
1/16	5/8	0.625	exact
1/32	5/8	0.625	exact
1/64	5/8	0.625	exact

Answer

0.625 = 5/8

Quick answers

How do you convert a decimal to a fraction?: Write the digits after the point over 1 followed by as many zeros as there are decimal places, then divide top and bottom by their greatest common divisor. 0.75 has two places, so it is 75/100, and dividing both by 25 gives 3/4.
What is 0.625 as a fraction?: 5/8. Three decimal places give 625/1000, and the greatest common divisor of 625 and 1000 is 125, so the fraction reduces to 5/8. On a tape measure it is exactly five eighths of an inch.
What is 0.333 repeating as a fraction?: 1/3. Enter it as 0.(3). Typing 0.333 without brackets means exactly three decimal places, which is 333/1000, a slightly smaller number.
What is 0.1666 repeating as a fraction?: 1/6. Enter it as 0.1(6), with only the repeating 6 in brackets. The working is 100x - 10x = 16 - 1, so 90x = 15 and x = 15/90, which reduces to 1/6.
What is 0.3 inches as a fraction on a tape measure?: About 5/16 inch. The exact fraction is 3/10, which is not a ruler mark. The nearest sixteenth is 5/16 (0.3125), 0.0125 inch too big, and the nearest sixty-fourth is 19/64, 0.003125 inch too small.
Can every decimal be written as a fraction?: Every decimal that ends or repeats can. Decimals that go on forever without a repeating pattern, such as pi or the square root of 2, are irrational and have no exact fraction, only close ones like 355/113 for 3.14159.

Why use Decimal to Fraction Converter

This converter turns a decimal into an exact fraction and shows the working. A terminating decimal is written over a power of ten and reduced, so 0.625 becomes 625/1000 and then 5/8. A repeating decimal is entered with the repeating digits in brackets, so 0.1(6) becomes 1/6 and 0.(3) becomes 1/3. Values above 1 are also given as a mixed number: 2.75 is 11/4, or 2 3/4. The Nearest fraction option adds the closest practical fraction, such as the nearest 1/16 for reading a decimal inch measurement on a tape measure, and says how far off it is. The conversion uses whole-number arithmetic, so nothing is rounded unless you ask for it.

Decimal to fraction chart for common values

Every row is the converter's output. Brackets mark repeating digits. The last column is the nearest sixteenth, for inch measurements.

Decimal	Fraction	Percent	Nearest 1/16
0.05	1/20	5%	1/16
0.0625	1/16	6.25%	1/16 (exact)
0.08(3)	1/12	8.(3)%	1/16
0.1	1/10	10%	1/8
0.(1)	1/9	11.(1)%	1/8
0.125	1/8	12.5%	1/8 (exact)
0.(142857)	1/7	14.(285714)%	1/8
0.15	3/20	15%	1/8
0.1(6)	1/6	16.(6)%	3/16
0.2	1/5	20%	3/16
0.25	1/4	25%	1/4 (exact)
0.3	3/10	30%	5/16
0.3125	5/16	31.25%	5/16 (exact)
0.(3)	1/3	33.(3)%	5/16
0.375	3/8	37.5%	3/8 (exact)
0.4	2/5	40%	3/8
0.45	9/20	45%	7/16
0.5	1/2	50%	1/2 (exact)
0.6	3/5	60%	5/8
0.625	5/8	62.5%	5/8 (exact)
0.(6)	2/3	66.(6)%	11/16
0.7	7/10	70%	11/16
0.75	3/4	75%	3/4 (exact)
0.8	4/5	80%	13/16
0.8(3)	5/6	83.(3)%	13/16
0.875	7/8	87.5%	7/8 (exact)
0.9	9/10	90%	7/8
1.25	5/4 = 1 1/4	125%	1 1/4 (exact)
1.5	3/2 = 1 1/2	150%	1 1/2 (exact)
2.75	11/4 = 2 3/4	275%	2 3/4 (exact)

0.33 and 0.67 are not thirds: 0.33 is exactly 33/100 and 0.67 is exactly 67/100. Use 0.(3) and 0.(6) for 1/3 and 2/3.

Tenths of an inch as ruler fractions

Decimal inches from a calculator, drawing or digital caliper rarely land on a ruler mark. These are the closest marks at each precision.

Decimal inches	Nearest 1/8	Nearest 1/16	Nearest 1/32	Nearest 1/64
0.1	1/8	1/8	3/32	3/32
0.2	1/4	3/16	3/16	13/64
0.3	1/4	5/16	5/16	19/64
0.4	3/8	3/8	13/32	13/32
0.5	1/2	1/2	1/2	1/2
0.6	5/8	5/8	19/32	19/32
0.7	3/4	11/16	11/16	45/64
0.8	3/4	13/16	13/16	51/64
0.9	7/8	7/8	29/32	29/32
1.4	1 3/8	1 3/8	1 13/32	1 13/32
2.65	2 5/8	2 5/8	2 21/32	2 21/32
5.3	5 1/4	5 5/16	5 5/16	5 19/64

A value exactly halfway between two marks is rounded up. Fractions are simplified, so 6/32 is shown as 3/16.

The formula for terminating and repeating decimals

Terminating: digits / 10^n, where n is the number of decimal places. Repeating: (all digits through one repeat - digits before the repeat) / (10^n x (10^r - 1)), where n is the count of non-repeating places and r is the length of the repeat. Then divide both parts by their GCD.

For 0.1(6), n is 1 and r is 1: the digits through one repeat are 16 and the digits before the repeat are 1, so the fraction is (16 - 1)/(10 x 9) = 15/90 = 1/6. For 1.2(34), n is 1 and r is 2, giving (1234 - 12)/(10 x 99) = 1222/990 = 611/495. The rule comes from algebra: multiplying x by two different powers of ten lines up the repeating tails so that subtracting one from the other cancels them. A pure repeat such as 0.(142857) simply sits over as many nines as it has digits: 142857/999999, which reduces to 1/7.

Worked conversions

A terminating decimal

Decimal 0.625; Nearest fraction Nearest 1/16

5/8. Before simplifying 625/1000, divided top and bottom by 125. Nearest 1/16: 5/8, exact. Percent 62.5%.

A decimal greater than 1

Decimal 2.4375; Nearest fraction Nearest 1/4

39/16 = 2 7/16. Before simplifying 24,375/10,000, divided by 625. Nearest 1/4: 2 1/2, which is 0.0625 too big.

A repeating decimal with a non-repeating start

Decimal 1.2(34); Nearest fraction Closest with denominator up to 100

611/495 = 1 116/495. The closest fraction with a denominator up to 100 is 1 15/64, 0.000032 too big.

A negative decimal

Decimal -1.75; Nearest fraction Nearest 1/8

-7/4 = -1 3/4. Nearest 1/8: -1 3/4, exact.

A long decimal approximated by a small fraction

Decimal 3.14159; Nearest fraction Closest with denominator up to 1,000

Exact: 314,159/100,000, already in lowest terms. Closest with a denominator up to 1,000: 3 16/113 (that is 355/113), 0.000003 too big. With a limit of 10 it is 3 1/7.

A percent

Decimal 12.5%; Nearest fraction Nearest 1/16

1/8. A trailing percent sign divides by 100 first: 125/1000 reduces to 1/8.

Ruler fractions versus the closest fraction of any denominator

The two groups in the Nearest fraction menu answer different questions. A ruler option rounds to the closest multiple of one division, 1/2, 1/4, 1/8, 1/16, 1/32 or 1/64, and then simplifies it. This is the one to use for inches, drill bits and wrench sizes, where only those denominators exist. The Nearest ruler fractions table lists all six at once with the size and direction of the error, so you can decide whether a sixteenth is close enough or the job needs a sixty-fourth.

The Any denominator options find the single closest fraction whose denominator does not exceed 10, 100 or 1,000. This is how a measured or rounded value is traced back to a simple ratio: 0.714 gives 5/7 with a limit of 10, and 0.33 gives 1/3. It cannot know what you meant, so treat the result as a suggestion and check the difference shown beside it.

A few limits apply. Recurring digits must be marked with brackets; a row of dots such as 0.333... is rejected rather than guessed at. Numbers are limited to 30 digits. A decimal comma such as 0,75 is read as 0.75. To go the other way, from a fraction to a decimal, use the fraction calculator, which shows the decimal for any fraction you enter.

How to use it

1
Type the number in the Decimal box, for example 0.625, 1.75 or -0.4.
2
For a repeating decimal, put the repeating digits in brackets: 0.(3) for 0.333... or 0.1(6) for 0.1666...
3
Choose a Nearest fraction option: a ruler fraction from 1/2 to 1/64, or the closest fraction with a denominator up to 10, 100 or 1,000.
4
Read the Fraction and Mixed number, then the Working, step by step table to see the GCD used.
5
Check the Nearest ruler fractions table for the value rounded to each ruler division and the difference from the exact value.

Common questions

How do I type a repeating decimal?

Wrap only the digits that repeat in brackets. 0.(3) is 0.333..., 0.1(6) is 0.1666..., 0.(09) is 0.090909... and 0.(142857) is one seventh. Digits before the bracket are treated as occurring once.

How do I convert a decimal to a mixed number?

Keep the whole part and convert only the digits after the point. For 2.75, the 2 stays and 0.75 becomes 3/4, giving 2 3/4. The converter shows this next to the improper fraction 11/4.

Why is 0.33 shown as 33/100 instead of 1/3?

Because 0.33 is exactly thirty-three hundredths, and the exact answer is always given first. Enter 0.(3) if you mean one third, or choose Closest with denominator up to 10 to see 1/3 offered as the nearby simple fraction.

How do I find the nearest 1/16 of an inch by hand?

Multiply the decimal part by 16, round to the nearest whole number and put that over 16, then simplify. For 0.3: 0.3 x 16 = 4.8, which rounds to 5, so the answer is 5/16. Use 32 or 64 in place of 16 for finer marks.

Is 0.(9) really equal to 1?

Yes. The converter returns 1 for 0.(9), because the working gives 9/9. A decimal of endless nines is another way of writing the next number up, in the same way that 0.(3) is another way of writing 1/3.

Which decimals terminate and which repeat?

A fraction in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5. Halves, quarters, eighths, fifths and tenths terminate; thirds, sixths, sevenths, ninths and elevenths repeat.

Does the converter accept negative numbers and whole numbers?

Yes. A minus sign carries through to the fraction and mixed number, so -1.75 gives -7/4. A whole number such as 2 is returned unchanged, as 2/1 before simplifying.