Question

without actually performing long division state weather the following rational number will have a terminating decimal expainsion or a non terminating repeating expainsion
1) 238 23/8
2) 38 3/8
3) 125441 125/441
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Answer 1

Answer:

1)Terminating

2) Terminating

3)Non Terminating

Step-by-step explanation:

To know if the number is terminating we need to find the prime factors of the denominator.

If the denominator is in the form 2^n x 5^m, then it is terminating else it is not

1) 238 23/8

= 238 23/2^3

Thus it is terminating

2) 38 3/8

= 38 3/2^3

Thus it is terminating

3) 125441 125/441

= 125441 125/ 3 x 3 x 7 x 7

= 125441 125/3^2 x 7^2

Thus it is not terminating