Question

Without actual division decide which of following rational numbers have terminating decimal representatio.
33
——
375​

Answer 1

Step-by-step explanation:

Given:-

33/375

To find:-

Without actual division decide the following rational number have terminating decimal .

Solution:-

Given that

33/375

It can be written as (3×11)/(3×125)

=> 11/125

=> 11/5^3

We know that

The rational number X is a terminating decimal if the denominator of X is in the form of 2^m × 5^n

On multiplying the numerator and the denominator with 2^3

=> (11/5^3)×(2^3/2^3)

=> (11×2^3)/(5^3×2^3)

=> (11×8)/(2×5)^3

=> 88/10^3

=> 88/1000

=> 0.088

33/375 = 0.088 is a terminating decimal.

Answer:-

33/375 is a terminating decimal

33/375 = 0.088

Used formulae:-

• The rational number X is a terminating decimal if the denominator of X is in the form of 2^m × 5^n