How do you convert a fraction to a decimal?

Divide the numerator by the denominator. For 3/8, 3 ÷ 8 = 0.375. For a mixed number such as 1 3/8, convert the fraction part and add the whole number, which gives 1.375. The converter on this page shows each long division step.

Why is 1/3 written as 0.333... and how do I show it exactly?

The division never ends: every step leaves remainder 1, so the 3 repeats forever. Write it with a bar over the 3, or as 0.(3) in brackets. A rounded 0.333 is only an approximation. As a fraction, 0.(3) is exactly 1/3.

Which fractions give repeating decimals?

A fraction in lowest terms repeats when its denominator has a prime factor other than 2 or 5. Up to 12 the repeating denominators are 3, 6, 7, 9, 11, 12. For example 1/7 = 0.(142857) has a block of 6 digits. Denominators 2, 4, 5, 8, 10 end.

How do I convert a decimal like 0.375 or 0.(3) to a fraction?

For 0.375, write 375/1000 and reduce it to 3/8. For a repeating decimal, multiply to line up the repeats and subtract: 0.(3) = 1/3 and 0.1(6) = 1/6. The converter does both and shows the percent.

What is 7/64 as a decimal and in millimetres?

7/64 inch is 0.109375 inch. At 25.4 mm per inch that is 2.778 mm rounded to 3 places. The inch tab lists every 64th from 1/64 to 64/64, and the nearest-64th finder turns a decimal or mm value into the closest fraction.

Can I print the fraction to decimal chart for free?

Yes. The Printables tab exports the chart, the inch table, the repeating decimals sheet, the strips and number line sheet and the decimal to fraction chart as PNG, SVG or print, on A4 or US Letter, in color or black and white. Everything is free and needs no account.

Math Reference

Fraction to Decimal Chart

Fraction to decimal chart from halves to 64ths with repeating decimals marked, percent, inch to mm, a two-way converter and printable A4 and Letter sheets.

Halves to twelfths with exact decimals, repeating parts markedFraction to decimal and decimal to fraction, with percentInch fractions 1/64 to 1 with decimal inches and mmPNG, SVG and print sheets, A4 or Letter, no sign-up

Denominator (pick one or more)

Order

Include fractions not in lowest terms

Fraction to decimal chart, denominators 2 to 12
Fraction	Decimal (exact)	Rounded to 3 places	Percent	Type
1/2	0.5	0.500	50%	ends
1/3	0.3	≈ 0.333	≈33.33%	repeats, 1 digit
2/3	0.6	≈ 0.667	≈66.67%	repeats, 1 digit
1/4	0.25	0.250	25%	ends
3/4	0.75	0.750	75%	ends
1/5	0.2	0.200	20%	ends
2/5	0.4	0.400	40%	ends
3/5	0.6	0.600	60%	ends
4/5	0.8	0.800	80%	ends
1/6	0.16	≈ 0.167	≈16.67%	repeats, 1 digit
5/6	0.83	≈ 0.833	≈83.33%	repeats, 1 digit
1/7	0.142857	≈ 0.143	≈14.29%	repeats, 6 digits
2/7	0.285714	≈ 0.286	≈28.57%	repeats, 6 digits
3/7	0.428571	≈ 0.429	≈42.86%	repeats, 6 digits
4/7	0.571428	≈ 0.571	≈57.14%	repeats, 6 digits
5/7	0.714285	≈ 0.714	≈71.43%	repeats, 6 digits
6/7	0.857142	≈ 0.857	≈85.71%	repeats, 6 digits
1/8	0.125	0.125	12.5%	ends
3/8	0.375	0.375	37.5%	ends
5/8	0.625	0.625	62.5%	ends
7/8	0.875	0.875	87.5%	ends
1/9	0.1	≈ 0.111	≈11.11%	repeats, 1 digit
2/9	0.2	≈ 0.222	≈22.22%	repeats, 1 digit
4/9	0.4	≈ 0.444	≈44.44%	repeats, 1 digit
5/9	0.5	≈ 0.556	≈55.56%	repeats, 1 digit
7/9	0.7	≈ 0.778	≈77.78%	repeats, 1 digit
8/9	0.8	≈ 0.889	≈88.89%	repeats, 1 digit
1/10	0.1	0.100	10%	ends
3/10	0.3	0.300	30%	ends
7/10	0.7	0.700	70%	ends
9/10	0.9	0.900	90%	ends
1/11	0.09	≈ 0.091	≈9.09%	repeats, 2 digits
2/11	0.18	≈ 0.182	≈18.18%	repeats, 2 digits
3/11	0.27	≈ 0.273	≈27.27%	repeats, 2 digits
4/11	0.36	≈ 0.364	≈36.36%	repeats, 2 digits
5/11	0.45	≈ 0.455	≈45.45%	repeats, 2 digits
6/11	0.54	≈ 0.545	≈54.55%	repeats, 2 digits
7/11	0.63	≈ 0.636	≈63.64%	repeats, 2 digits
8/11	0.72	≈ 0.727	≈72.73%	repeats, 2 digits
9/11	0.81	≈ 0.818	≈81.82%	repeats, 2 digits
10/11	0.90	≈ 0.909	≈90.91%	repeats, 2 digits
1/12	0.083	≈ 0.083	≈8.33%	repeats, 1 digit
5/12	0.416	≈ 0.417	≈41.67%	repeats, 1 digit
7/12	0.583	≈ 0.583	≈58.33%	repeats, 1 digit
11/12	0.916	≈ 0.917	≈91.67%	repeats, 1 digit

Decimals are exact: digits under a red bar repeat forever. A leading ≈ marks a value rounded half up (3 places, or 2 places for percent). Showing 45 fractions.

Free Fraction to Decimal Charts and Printables

Every sheet below is drawn from the same computed values as the tables above. View, download and print them free, no sign-up.

Full chart

Fraction to Decimal Chart: Halves to Twelfths

All 45 fractions in lowest terms with denominators 2 to 12, exact decimals and percent.

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Charts

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Study aids

How to convert a fraction to a decimal

A fraction is a division. To turn 3/8 into a decimal, divide the top by the bottom: 3 ÷ 8 = 0.375. Use long division, adding a zero after the decimal point each time you run out of digits. If the remainder reaches 0, the decimal ends. For 5/16 you get 0.3125, and for 7/64 you get 0.109375.
For a mixed number such as 1 3/8, convert the fraction part and add the whole number, or turn it into an improper fraction (11/8) and divide. The converter above accepts both forms and shows the long division step by step.

Why some fractions repeat

Long division only has so many possible remainders. If a remainder comes back, the digits after it come back too, and the decimal repeats forever. A fraction in lowest terms ends only when its denominator has no prime factor except 2 and 5, the factors of 10. Among denominators up to 12, 2, 4, 5, 8, 10 give ending decimals and 3, 6, 7, 9, 11, 12 repeat. For example 1/3 = 0.(3), 1/6 = 0.1(6) and 1/7 = 0.(142857), a block of 6 digits. A block can never be longer than the denominator minus 1.

How to write a repeating decimal

Put a bar over the digits that repeat, as in the chart, or write them in brackets, such as 0.(3) for 0.333... A bar is exact; a rounded value like 0.333 is not. When you round, say so: 1/3 ≈ 0.333 to three places. Only the digits under the bar repeat, so 1/6 is 0.1 followed by a repeating 6, written 0.1(6), not 0.(16).

How to convert a decimal to a fraction

For an ending decimal, write the digits over 10, 100 or 1000 and reduce: 0.375 = 375/1000 = 3/8. For a repeating decimal, call it x and multiply by a power of 10 that moves one full repeating block past the point: 10 if one digit repeats, 100 if two, 1,000,000 if six. Then subtract. With x = 0.(3), 10x − x = 3, so 9x = 3 and x = 1/3. With x = 0.1(6), 100x − 10x = 15, so 90x = 15 and x = 1/6.
The decimal to fraction converter does this exactly. Type 0.(3) or 0.1(6) for a repeating decimal. If you type dots, such as 0.333..., the converter reads a visible repeating block as repeating and tells you so. A plain 0.333 is the exact fraction 333/1000, so the tool also shows the closest simple fraction.

Inch fractions in the shop: decimals and millimetres

Woodworkers and DIY builders read rulers and tape measures in 8ths, 16ths, 32nds and 64ths, while drawings and machine settings often use decimal inches. This chart converts between the two, and the inch tab lists all 64 values. The smallest step, 1/64 in, is 0.015625 in, or about 0.397 mm. Three eighths is 0.375 in, exactly 9.525 mm, and 7/64 in is 0.109375 in, which is 2.778 mm to three places. Every inch fraction with a power of 2 in the denominator ends as a decimal, so decimal inches are exact. Millimetres use 1 inch = 25.4 mm and are rounded half up, so check your tolerance before you cut. The nearest-64th finder turns a decimal or a metric length into the closest ruler fraction and shows the error.

Fraction, decimal and percent together

Percent is the decimal times 100, so 0.375 is 37.5% and 0.(3) is 33.(3)%. The chart prints percent with the fraction and decimal so one lookup gives all three forms. To see why the values line up, compare fraction strips and number lines: 1/2, 2/4 and 4/8 sit at the same point, 0.5. The strips and number line sheet in the gallery draws this.