Fraction to decimal calculator

To convert a fraction to a decimal, divide the numerator by the denominator. For 3/8, 3 ÷ 8 = 0.375. By long division, 8 goes into 30 three times with 6 left over, into 60 seven times with 4 left over, and into 40 five times exactly.

Some fractions never end. 5/12 is 0.41666..., with the 6 repeating forever, written 0.41(6) with the repeating block in brackets, or with a bar over the 6 in a textbook. Long division shows why: once a remainder comes back, the digits after it repeat, and there are only as many possible remainders as the denominator allows.

Which ones end is decided by the denominator. A fraction in lowest terms gives a terminating decimal exactly when its denominator has no prime factors except 2 and 5. 3/8 ends because 8 = 2 × 2 × 2, and 7/20 ends because 20 = 2 × 2 × 5. 1/3, 1/6, 1/7 and 5/12 repeat, because 3 or 7 divides the denominator.

For a mixed number, convert the fraction part and add the whole number: 2 3/8 = 2 + 0.375 = 2.375. For a percentage, multiply the decimal by 100: 3/8 is 37.5%.