Question

$\huge \mathfrak \pink{bonjour}$
After how many decimal places will the decimal expansion of
2/2³×2⁴ terminate?​

Answer 1

4

Step-by-step explanation:

2⁴ = 16

5³ = 125

Thus, 2⁴ X 5³ = 16 X 125 = 2000

As per the question,

23/(2⁴ X 5³) = 23/2000 = 0.0115

Therefore, after 4 decimal places the decimal expansion of 23/(2⁴ X 5³) terminates.

MARK ANSWER AS BRAINLIEST

Answer 2

$\frac{2}{2^{4} { \times 2}^{3}} = \frac{2}{2 ^{3 + 4} } = \frac{2}{2 {}^{7} } = \frac{2 \times {5}^{7} }{ {2}^{7} \times {5}^{7} } = \frac{2 \times {5}^{7} }{ {10}^{7} } \\ \\ \\ hence \: the \: fraction \: will \: terminate \: after \: 7 \: decimals...... \\ \\ please \: mark \: it \: as \: brainliest$