Question

a decimal expansion of 23/2^5×5^2 will terminate after how many places of decimal ??​

Answer 1

0.02875.

It terminates after 5 places of decimal.

Explanation:

We have to get the decimal expansion of $\frac{23}{2^{5}\times 5^{2}}$.

So, we will get the decimal expansion after dividing 23 with $(2^{5} \times 5^{2})$.

Now, $2^{5} = 2 \times 2 \times 2 \times 2 \times 2 = 32$ and $5^{2} = 5 \times 5 = 25$

Therefore, the expression will be

$\frac{23}{2^{5}\times 5^{2}} = \frac{23}{32 \times 25} = \frac{23}{800} = 0.02875$

Therefore, the decimal expansion of the given expression is 0.02875 and it terminates after 5 places of decimal. (Answer)

Answer 2

The decimal expansion is 0.02875

Given:

23/(2⁵ × 5²)

Explanation:

2⁵ = 2 × 2 × 2 × 2 × 2 = 32

5² = 5 × 5 = 25

Now,

2⁵ × 5² = 32 × 25 = 800

Now,

23/800 = 0.02875

The numerator is less than the denominator, thus, the decimal value with 0. is obtained.