Question

decimal expansion of 9/125 will ter
minate after how many places of decimals

Answer 1

Hey mate..
=========

Given,

$\frac{9}{125} \\ \\ = \frac{9}{5 \times 5 \times 5} \\ \\ = \frac{9}{5 {}^{3} } \\ \\ = \frac{9 \times 2 {}^{3} }{5 {}^{3} \times 2 {}^{3} } \\ \\ = \frac{9 \times 8}{(5 \times 2) {}^{3} } \\ \\ = \frac{72}{10 {}^{3} } \\ \\ = \frac{72}{1000} \\ \\ = 0.072$


So,

The given rational number will terminate after 3 decimal places.

#racks

Answer 2

The rational number $\frac{9}{125}$ will terminate after 3 decimal places.

Step-by-step explanation:

Given : Decimal expansion of  $\frac{9}{125}$ will terminate.

To find : Terminate after how many places of decimals ?

Solution :

We can re-write the number as,

$\frac{9}{125}=\frac{9}{5 \times 5 \times 5}$

$\frac{9}{125}=\frac{9\times 2^3}{2^3\times 5^3}$

$\frac{9}{125}=\frac{9\times 8}{(2\times 5)^3}$

$\frac{9}{125}=\frac{72}{(10)^3}$

$\frac{9}{125}=0.072$

The rational number $\frac{9}{125}$ will terminate after 3 decimal places.

#Learn more

Write a decimal expansion of3/13 and what kind of decimal expansion is this​

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