- How do you convert a fraction to a decimal by hand?
- Divide the top number by the bottom number with long division. For 3/8, 8 doesn't go into 3, so write 0. and bring down a zero: 8 goes into 30 three times (24), leaving 6. Bring down another zero: 60 ÷ 8 is 7 (56), leaving 4. Then 40 ÷ 8 is exactly 5 with nothing left over. So 3/8 = 0.375. When the remainder hits zero, the decimal stops.
- How do I convert a mixed number like 2 3/4 to a decimal?
- Keep the whole number and convert only the fraction. 3/4 is 0.75, so 2 3/4 is 2.75. For a negative mixed number, the minus applies to the whole thing: -2 3/4 is -2.75, not -1.25. You can also turn it into an improper fraction first — 2 3/4 = 11/4 — and divide 11 by 4 to get the same 2.75.
- Why do some fractions repeat forever?
- Reduce the fraction, then look at the bottom number. If its only prime factors are 2 and 5, the decimal stops: 7/20 = 0.35 because 20 = 2 × 2 × 5. Any other prime makes it repeat: 1/3 = 0.333…, 1/6 = 0.1666…, 1/7 = 0.142857142857…. Our decimals are base 10, and 10 = 2 × 5, so only those two primes divide evenly. During long division a repeating fraction keeps landing on remainders it has already seen, and once a remainder repeats, every digit after it does too.
- What does the bar over a decimal mean?
- The bar marks the digits that repeat forever. 0.16̄ means 0.16666…, where only the 6 repeats. 0.1̄6̄ would mean 0.161616…. Some textbooks write the same thing with brackets, 0.1(6), or with dots over the first and last repeating digit. All three say the same thing; the converter shows the bar in the result and names the repeating digits in words underneath.
- How long can the repeating part of a decimal be?
- For a fraction with bottom number q, the repeat is at most q − 1 digits long. 1/7 repeats every 6 digits, 1/17 every 16, and 1/97 every 96. 1/983 repeats a block of 982 digits. The converter finds repeats up to 1,000 digits long; past that it shows the first digits and the rounded value and tells you the repeat is too long to write out.
- What are common fractions as decimals?
- 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875, and 1/16 = 0.0625. The thirds and sixths repeat: 1/3 = 0.333…, 2/3 = 0.666…, 1/6 = 0.1666…, and 5/6 = 0.8333…. A table of these sits under the converter.
- How is the decimal rounded?
- To the number of places you pick, with halves rounded away from zero — the way most schools teach it. 1/8 is 0.125, so to 2 places it's 0.13, and -1/8 is -0.13. Trailing zeros are dropped, so 1/2 to 4 places shows 0.5. If rounding changes the value, you'll see a "Rounded to" line; if the decimal fits within your places, it isn't shown.
- How do I turn a fraction into a percent?
- Convert it to a decimal, then multiply by 100 — move the decimal point two places right. 3/8 = 0.375 = 37.5%. 1/3 = 0.333… = 33.33…%, which rounds to 33.3333% at 4 places. The converter shows the percent under every result, rounded to the same number of places as the decimal.
- Why does my calculator show 0.3333333333333333 for 1/3?
- Calculators and spreadsheets store numbers in binary floating point, which holds about 16 significant digits, so they cut the repeat off and sometimes the last digit is slightly wrong. This converter does the long division digit by digit with whole numbers, so every digit it shows is correct, and it tells you when the decimal repeats instead of pretending it stops.
- Is what I type saved or sent anywhere?
- No. The conversion runs in your browser. Nothing is sent to a server or stored, and closing the tab clears it.
