Terminating Decimals Calculator

The method

decimal = numerator ÷ denominator

Which fractions terminate

A fraction in lowest terms gives a terminating decimal exactly when its denominator factors into nothing but 2s and 5s — the primes of ten. So 1/8 and 3/20 terminate, while 1/3, 1/7 and 1/12 recur forever. That is a property of base ten, not of the fraction: 1/3 terminates neatly in base 3.

The rules in one place

• Adding and subtracting needs a common denominator first. The lowest common denominator keeps the numbers smallest, but any common denominator works.
• Multiplying needs no common denominator at all — multiply across the top and across the bottom.
• Dividing means multiplying by the reciprocal: flip the second fraction and multiply.
• Reducing divides top and bottom by their greatest common divisor. It never changes the value.

Why lowest terms matter

6/8 and 3/4 are the same number, but 3/4 is easier to compare, easier to check and conventional in an answer. Reducing also keeps later arithmetic small: multiplying unreduced fractions makes the numbers grow fast, and cancelling first avoids that.