Question

After how many decimal places expression will terminate 4^7/ 2³× 5²

Answer 1

Answer:

Step-by-step explanation:

23/2^4 x 5^3 = (23x5)/2^4 x 5^4 making the powers of 2 and 5 in the denominator equal, so that we get 115/10^4 = 115/10000= 0.0115.

So, the decimal expansion gets terminated with number of decimal places as much as the power of 10.

Note: A rational number will give a terminating decimal only if the denominator is a product of various powers of 2 and 5.

Otherwise, we get a recurring decimal.

Answer 2

Solution :

Given rational number

$\frac{4^{7}}{\left(2^{3} \cdot5^{2}\right)}$

= $\frac{4^{7} \cdot 5}{\left(2^{3}\cdot5^{3}\right)}$

=$\frac{4^{7}\cdot5}{\left(2\cdot5\right)^{3}}$

=$\frac{4^{7}\cdot5}{\left(10\right)^{3}}$

=$\frac{4^{7}\cdot5}{\left(1000\right)}$

$\rm\textsf{Therefore}$

$\rm\textsf{After \:Three \:decimal \:places \:given \: expression\: terminates.}$

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