Question

After how many decimal representation of the rational number 229/(2*2*5*5*5*5*5*5*5)terminate​

Answer 1

After how many decimal

places will the decimal

representation of the

${ 229 }$ rational number -

terminate ? ${2² × 5^7}$

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,

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

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

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

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

$\space{=> 0.0007328}$

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