Question

Without performing division,state whether the following numbers will have a terminating decimal form or non terminating repeating decimal form

1) 64/455​

Answer 1

Answer:

Answer

Given rational number is

455

64

q

p

is terminating if

a) p and q are co-prime and

b) q is of the form of 2

n

5

m

where n and m are non-negative integers.

Firstly we check co-prime,

64=2

6

455=5∗7∗13

⇒64 and 455 have no common factors.

Therefore, 64 and 455 are co-prime.

Now, we have to check that q is in the form of 2

n

5

m

.

455=5∗7∗13

So, denominator is not of the form 2

n

5

m

.

Thus,

455

64

is a non-terminating repeating decimal.

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