Fraction to Decimal Calculator

Welcome to the Fraction to Decimal Calculator

Fractions, decimals and percents are three ways of writing the same amount. This fraction to decimal calculator converts in both directions and shows the work. In one direction, type a fraction or a mixed number and the calculator divides the numerator (the top number) by the denominator (the bottom number) with the long division written out, marks any digits that repeat with a bar, and gives the percent as well. In the other direction, type a decimal — including a negative decimal or a repeating one — and the calculator writes it over a power of ten, reduces it to lowest terms, and shows the mixed-number form when the value is bigger than one.

Use the two buttons at the top of the calculator to choose the direction. The calculator opens on 3/8, a fraction whose long division stops after three digits, so you can see every step of the method before trying your own. Each conversion gets a link in the “Share This Conversion” panel that reopens the calculator exactly as you left it.

If you only need a quick answer for a common value — what 0.8 is as a fraction, or what 5/16 is as a decimal — skip to the table of common conversions further down the page. Every row there was produced by the same method the calculator uses.

How to Convert a Fraction to a Decimal

A fraction bar is a division sign: 3/8 means 3 ÷ 8. To convert a fraction to a decimal, divide the numerator by the denominator with long division, bringing down a zero each time the remainder is not zero. Take 3/8. Eight does not go into 3, so the decimal starts 0. and we bring down a zero: 8 goes into 30 three times (24) with 6 left over. Bring down another zero: 8 goes into 60 seven times (56) with 4 left over. Once more: 8 goes into 40 exactly five times with nothing left. The remainder is 0, so the division stops, and 3/8 = 0.375.

A mixed number converts the same way with the whole part carried in front. For 1 3/4, the fraction part 3/4 is 0.75, so 1 3/4 = 1.75. The calculator makes the mixed number improper first (7/4) and divides, which gives the same result and keeps the method uniform. A remainder of 0 means the decimal terminates; if the remainders never reach 0 you have a repeating decimal, covered next.

Repeating Decimals

Some fractions never divide out evenly. For 2/3, 3 goes into 20 six times with 2 left over — and then into 20 again, and again, forever. Whenever a remainder you have already seen comes back, the digits from that point repeat. We write a repeating decimal with a bar over the repeating block: 2/3 = 0.6, read “zero point six repeating”. The block can be longer than one digit, as with 1/7 = 0.142857, and it can start after some digits that do not repeat, as with 1/6 = 0.16.

A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5 — halves, quarters, fifths, eighths, tenths, sixteenths and so on. Any other denominator (thirds, sixths, sevenths, ninths, twelfths) produces a repeating decimal. The calculator shows the repeating block with a bar and also gives a rounded value, such as 0.6667 for 2/3, for when you need a plain number.

How to Convert a Fraction to a Percent

Percent means “per hundred”, so a percent is just a decimal with the point moved two places to the right. Convert the fraction to a decimal first, then multiply by 100 and add the percent sign: 3/8 = 0.375 = 37.5%, and 1 3/4 = 1.75 = 175%. Repeating decimals keep their bar, so 2/3 = 66.6%, which is usually rounded to 66.7% or written as 66 2/3%. The calculator shows the percent as a separate step under the decimal, and the percentage calculator works the other problems percents turn up in, like finding a percentage of a number.

Decimal to Fraction Calculator

Switch the direction and this page works as a decimal to fraction calculator. The method uses place value. The first digit after the decimal point is tenths, the second is hundredths, the third is thousandths, so a decimal is the digits after the point written over a power of ten with the same number of zeros as there are decimal places. Take 0.8: the 8 is in the tenths place, so 0.8 = 8/10. Then reduce. The greatest common factor of 8 and 10 is 2, and dividing the top and the bottom by 2 gives 4/5. So 0.8 as a fraction is 4/5.

The fraction the calculator gives is always in lowest terms — it finds the greatest common factor of the numerator and denominator and divides both by it, showing that step. Two decimal places work the same way over 100: 0.16 = 16/100, and dividing by the greatest common factor 4 gives 4/25. Whole numbers are fractions over 1, so 3 becomes 3/1. When the decimal is bigger than one, as with 1.75 = 175/100 = 7/4, the calculator also writes the mixed number, 1 3/4.

Repeating Decimal to Fraction

A repeating decimal cannot be written over a power of ten, because it never ends. Instead, use a little algebra to make the repeating tail cancel. Call the decimal x. For 0.333…, multiply by 10 so one full repeat moves in front of the decimal point: 10x = 3.333…. Now subtract the original: 10x − x = 3.333… − 0.333… = 3, so 9x = 3 and x = 3/9, which reduces to 1/3.

When some digits before the repeat do not repeat, multiply twice. For 0.1666…, x = 0.1666…, 10x = 1.666… and 100x = 16.666…. Subtract the two lines that share the same tail: 100x − 10x = 16.666… − 1.666… = 15, so 90x = 15 and x = 15/90 = 1/6. Type the repeating digits in the box marked “repeating” (or in parentheses, like 0.1(6)) and the calculator writes out exactly these lines for your number.

Negative Decimals as Fractions

A negative decimal converts exactly like a positive one; the sign just rides along. Convert the number without its sign, then put a single minus sign in front of the whole answer. So −2.5 is 25/10, which reduces to 5/2, giving −5/2 — or −2 1/2 as a mixed number, since 2 goes into 5 twice with 1 left over. Use the sign button beside the input to make a number negative. The one mistake to avoid is writing the minus sign on both the numerator and the denominator, which would cancel out and make the fraction positive again.

Answers for Common Decimals and Fractions

The values below are the ones that come up most often in homework and everyday measuring. Each row shows the decimal, the fraction in lowest terms (with the mixed number when the value is bigger than one), the percent, and the one-line method for turning the decimal back into the fraction. A bar over digits means they repeat.

0.8 as a fraction is 4/5 (80%): write 0.8 as 8/10, divide both by 2.

0.6 as a fraction is 3/5 (60%): write 0.6 as 6/10, divide both by 2.

0.4 as a fraction is 2/5 (40%): write 0.4 as 4/10, divide both by 2.

0.16 as a fraction is 4/25 (16%): write 0.16 as 16/100, divide both by 4.

−2.5 as a fraction is −5/2, or −2 1/2 as a mixed number (−250%): write 2.5 as 25/10, divide both by 5, and keep the minus sign in front.

Need a value that is not in the table? Type it into the calculator above — the method is the same for every decimal and every fraction, and the fraction chart shows halves through sixteenths side by side if you want to see how the sizes compare.

Further Reading on Fractions and Decimals

• The visual fraction calculator adds, subtracts, multiplies and divides fractions and shows every answer as a decimal and a percent.
• The long division calculator animates the division method used here for whole-number problems with remainders.
• Repeating decimals at Wikipedia — why some fractions terminate and others repeat, with the full theory behind the 2-and-5 rule.