Terminating or Repeating?

Free interactive math game: Terminating or Repeating? — Which kind of decimal?. Part of the Decimal Fractions category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. Will 1/5 give a terminating or repeating decimal? 1/5
  2. Will 1/4 give a terminating or repeating decimal? 1/4
  3. Will 2/7 give a terminating or repeating decimal? 2/7
  4. Will 2/11 give a terminating or repeating decimal? 2/11

About this exercise

Deciding whether a fraction gives a decimal that stops or one that repeats.

How to solve it

Simplify first, then look at the denominator. If its only prime factors are 2 and 5, the decimal terminates. Any other factor makes it repeat.

Worked example

One eighth terminates because 8 is 2 x 2 x 2, while one third repeats.

Common mistake

Checking before simplifying. Six over twelve looks awkward but is just a half.