Terminating decimal
Input
3/8
Expected result
0.375, which is 37.5%
Calculators
Fraction to Decimal Calculator
Convert a fraction or mixed number to an exact decimal with the repeating digits marked, a rounded value and a percent, plus a printable chart.
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About this tool
The Fraction to Decimal Calculator divides the numerator by the denominator and shows the exact decimal: 3/8 = 0.375, and 1/7 = 0.142857 with a line over 142857 because that block repeats forever. It works by long division and remembers every remainder. When a remainder comes up a second time, the digits from that point repeat, which is how it marks 1/6 = 0.1(6) and 7/12 = 0.58(3). You also get the value rounded half up to the number of decimal places you choose, the percentage and the fraction in lowest terms. Mixed numbers such as 2 1/3 become improper fractions first. Below the calculator is a fraction to decimal chart of common fractions (halves, thirds, quarters, fifths, sixths, eighths, tenths, twelfths and sixteenths) that can switch to every 16th, 32nd or 64th and opens on a plain page for printing. Each part of a fraction can have up to 15 digits, and if a repeating block is longer than 1,000 digits only the first 1,000 are shown. It runs in your browser.
Why use it
Marks the exact repeating block, even long ones such as the 96 digits of 1/97, instead of cutting the decimal off.
Shows the long division with every remainder, so you can follow or check the working by hand.
Gives the exact decimal, a rounded value, the percentage and the simplified fraction together.
Includes a fraction to decimal chart, from common fractions to every 64th of an inch, that prints on a plain page.
Uses exact big-integer math, so long numerators and denominators do not cause rounding errors.
How to use
- Type a fraction such as 3/8, a mixed number such as 2 1/3 (whole number, space, fraction) or a negative fraction such as -7/12.
- Set how many decimal places the rounded value should have. The default is 4.
- Read the exact decimal; a line over digits marks the part that repeats forever.
- Follow the long division steps to see where each digit and remainder comes from.
- Scroll to the chart for common fractions, switch it to 16ths, 32nds or 64ths if you need them, and press Print chart for a paper copy.
When it helps
- Checking homework that asks whether a fraction gives a terminating or a repeating decimal.
- Converting a fractional inch such as 5/16 to 0.3125 for a caliper, a CAD drawing or a drill chart.
- Turning a fraction into a percentage for a report, such as 7/8 = 87.5%.
- Printing a fraction to decimal chart for a workshop wall or a classroom.
- Rounding a fraction to a set number of decimal places for a spreadsheet.
Examples
Repeating decimal
Input
1/7
Expected result
0.(142857); rounded to 4 places, 0.1429
Mixed number
Input
2 1/3
Expected result
7/3 = 2.(3); rounded to 4 places, 2.3333
Tips
- In lowest terms, a fraction ends as a decimal only if its denominator has no prime factors other than 2 and 5: 3/40 = 0.075 ends, while 1/12 = 0.08(3) repeats.
- Rounding goes half up, so 1/8 = 0.125 becomes 0.13 at 2 decimal places.
- Select any fraction in the chart to load it into the calculator with its long division.
- For machining and woodworking, switch the chart to Every 64th; reducible rows show the simpler form, such as 40/64 = 5/8.
- Type mixed numbers with a space between the parts, as in 2 1/3. A hyphenated form such as 2-1/3 is not accepted.
Frequently Asked Questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator: 3/8 means 3 ÷ 8, which is 0.375. For a mixed number, convert it to an improper fraction first, so 2 1/3 = 7/3 = 2.333…
How can I tell if a fraction gives a repeating decimal?
Simplify the fraction and look at the denominator. If its only prime factors are 2 and 5, the decimal ends; any other prime factor, such as 3 or 7, makes it repeat. 7/20 = 0.35 ends, while 5/6 = 0.8(3) repeats.
How does the calculator find the repeating part?
During long division it records each remainder. A remainder can only be a whole number from 1 to the denominator minus 1, so one must eventually come up again, and from there the digits cycle. For 1/6 the remainder 4 appears twice, so the 6 repeats: 0.1(6).
What does the line over the digits mean?
The line, called a vinculum, marks digits that repeat forever, so 0.1 with a line over the 6 means 0.1666…. Written with parentheses, the same number is 0.1(6), which is the form the Copy exact decimal button copies.
What is 1/3 as a decimal?
1/3 = 0.333…, written 0.(3) or with a line over the 3. Rounded to 4 decimal places it is 0.3333, and as a percentage it is 33.333…%.
How do I convert a fraction to a percentage?
Divide to get the decimal, then multiply by 100: 3/8 = 0.375 = 37.5%. The calculator rounds the percentage to the same number of decimal places as the rounded decimal and adds ≈ when it had to round.
Can I print the fraction to decimal chart?
Yes. Choose Common fractions, Every sixteenth, Every 32nd or Every 64th, then press Print chart. A plain black-on-white page with the chart opens and the print dialog starts; allow pop-ups if nothing opens.
Is there a size limit?
Each part of the fraction can have up to 15 digits. The calculator works out up to 1,000 decimal digits; if the repeating block is longer than that, it shows the first 1,000 and says so.
Explore the category
Glossary
- Vinculum
- The line drawn over the repeating digits of a decimal.
- Repeating block (period)
- The group of digits that repeats in a repeating decimal; 1/7 has the 6-digit period 142857.
- Improper fraction
- A fraction whose numerator is at least its denominator, such as 7/3.
- Round half up
- A rounding rule in which a dropped part of one half or more raises the last kept digit, so 0.125 becomes 0.13.
- Long division
- Dividing step by step, bringing down a 0 after the decimal point to get each new digit and remainder.
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