How do you turn a decimal into a fraction?
For a decimal that ends, write the digits over a power of ten and simplify. 0.75 = 75/100, and dividing top and bottom by 25 gives 3/4. The rule: as many zeros in the denominator as there are digits after the point (0.6 = 6/10, 0.375 = 375/1000), then reduce by the greatest common divisor. The calculator above does the reducing for you and shows the result in lowest terms.
How do you convert a repeating decimal?
Repeating decimals need algebra, not just a power of ten. For 0.333…, let x = 0.333…, multiply by 10 to get 10x = 3.333…, subtract to get 9x = 3, so x = 1/3. Each repeating block over the same number of nines gives the fraction: 0.did7=0.7777… = 7/9, 0.27 repeating = 27/99 = 3/11. This is the part most people get wrong by hand — the calculator handles it if you mark the decimal as repeating.
Converting decimal inches to a fraction
In the US, tape measures use fractions of an inch, so a decimal like 0.625″ needs to become 5/8″. The trick is to round to the nearest common fraction — usually a sixteenth. 0.625 is exactly 10/16 = 5/8; 0.1875 is 3/16; 0.4 rounds to 6/16 = 3/8. For woodworking and construction, converting the decimal your calculator spits out back into the nearest 1/16 or 1/32 is what lets you actually mark the cut.
Why simplify to lowest terms?
6/8 and 3/4 are the same value, but 3/4 is the standard way to write it and the form teachers, recipes and rulers expect. Simplifying means dividing the numerator and denominator by their greatest common divisor until they share no factors. It makes fractions easier to compare (is 7/8 or 11/16 bigger?) and to work with, which is why the calculator always returns the reduced form.
Repeating decimals are exact fractions; decimals shown as terminating are converted as written. Round to the nearest 1/16 or 1/32 for tape-measure work.
Frequently asked questions
What is 0.375 as a fraction?
3/8. 0.375 = 375/1000, and dividing top and bottom by 125 gives 3/8.
What is 0.666… as a fraction?
2/3. It's a repeating decimal: 0.666… equals 6/9, which reduces to 2/3.
How do you write 0.5 as a fraction?
1/2. 0.5 = 5/10 = 1/2. Similarly 0.25 = 1/4 and 0.2 = 1/5.
How do I convert a repeating decimal to a fraction?
Put the repeating block over the same number of nines and simplify: 0.7777… = 7/9, 0.181818… = 18/99 = 2/11. Mark the decimal as repeating in the calculator and it does this for you.
What is 0.625 inches as a fraction?
5/8 inch. 0.625 = 10/16 = 5/8, a common tape-measure fraction.