Question

If 278 by 2^3m has a terminating decimal expansion and m is a positive integer such that 2

Answer 1

Solution:

To find: 278 / 2^3 has a terminating decimal expansion

We know that at a fraction will have a terminating decimal expansion if the prime factorization of its denominator is in the form of 2^m*5^n

Also you should know that the fraction will have a terminating decimal expansion if the prime factorization of denominator is only

2^m or 5^n are there

And here in the given question 278 / 2^3

denominator = 2^3

=> 2^3 * 5^0 ( 5^0= 1 )

Thus, it has a terminating decimal expansion

Answer 2

Given: If 27823/2^3m has terminating decimal expansion and m is a positive integer.

We know if any fraction have terminating decimal expansion then they have denominator in form of 2a × 5b

So,

m  = 5  , As m lies between 2 and 9 ( 2 < m < 9 )