Question

Without actual division find the decimal expansion of following rational number 23/2^3 ×5^2

Answer 1

$\huge \frak{ \frac{23}{ {2}^{3} \times {5}^{2} } } \\ \\ \leadsto \: \: \frac{23 \times 5}{ {2}^{3} \times {5}^{2} \times 5 } \\ \\ \leadsto \: \: \frac{115}{ {2}^{3} \times {5}^{3} } \: \: = \frac{115}{ {(2 \times 5)}^{3} } \\ \\ \leadsto \: \: \frac{115}{ {10}^{3} } \: \: = \frac{115}{1000} \\ \leadsto \: \: \sf\red{0.115}$

Answer 2

Answer:

The answer to this is quite simple it is 0.115

Step-by-step explanation:

So, what are we supposed to do...

Simple. 23/ 2^3 × 5^3 needs to be multiplied by 5 in both the numerator and denominator. This is done because we want to get a multiple of ten in the denominator in order to easily find the decimal expansion .

By multiplying 5,

In the numerator we get 23×5 = 115

In the denominator we get 10^3= 1000

∴ 115/1000= 0.115

Thank you !!