Question

without actually dividing find whether the Decimal representation of the following rational number will be terminating or non terminating 23/8​

Answer 1

Answer:

the following rational number is terminating

Step-by-step explanation:

(i) Given : 23/8

23/ 2³

Here, the factors of the denominator 8  are 2³ , which is in the form

2ⁿ 5^m .

So , 23/8 has terminating  decimal expansion.

23/8 = 23 × 5³ /2³ × 5³

= 23 × 125 / (2×5)³

= 2875/10³

= 2875/1000

= 2.875  

Hence, the decimal expansion of 23/8 is 2.875.