Question

16.
After how many decimal places will the decimal representation of the
229
rational number - terminate ?
2² x 5 to the power 7?
​

Answer 1

It will terminate after 7 decimal expansion.

Answer 2

After 7 decimal places will the decimal representation of the rational number $\frac{229}{2^2\times 5^7}$ terminate.

Step-by-step explanation:

To find : After how many decimal places will the decimal representation of the rational number $\frac{229}{2^2\times 5^7}$ terminate ?​

Solution :

The rational number is represented as $\frac{229}{2^2\times 5^7}$

Multiply the numerator and denominator by $2^5$,

$=\frac{229\times 2^5}{2^2\times 2^5\times 5^7}$

$=\frac{229\times 32}{2^7\times 5^7}$

$=\frac{7328}{(2\times 5)^7}$

$=\frac{7328}{(10)^7}$

$=0.0007328$

After 7 decimal places will the decimal representation of the rational number $\frac{229}{2^2\times 5^7}$ terminate.

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