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Question

Which of the following rational number can be represented as terminating and which as non terminating decimals? give the answer without actual dividing

1- 13/8

2-     -7/15


Solution

Let, N is Numerator and D is Denominator.

I believe the value of N ÷ D will NOT be a repeating decimal if and only if D is any of the following

  1. D is equal to 1 OR
  2. D's prime factors only consist of 2's and/or 5's. (includes all multiples of 10)

Otherwise, if none of the two rules above hold true, then the positive whole numbers N and D will divide into repeating decimal.

Here,
1) 13/8
8 has only one prime factor whic is 2.
so it is a terminating decimal
2)7/15
15 has prime 3 factor 5 which is neither 2 nor 5 .so it is a repeating decimal

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