Question

state whether the following terminating decimal representation or not 51/125

Answer 1

HEY THERE!!


Question:-

State whether the following terminating decimal representation or not 51/125.

Method of Solution:-

Given:-

Given Number = 51/125

So, 125 = 5³ and 5 is not a factor of 51.

•°• the given number in it's Simplest Form in the number .

Now, 5³ representation in the form of 2^m × 5^n

Where, m = 0 , n = 4,

So, the given number be terminating decimal.

•°•
$\frac{51}{125} = \frac{51}{ {5}^{3} } = \frac{51 \times {2}^{3} }{ {5}^{3} \times {2}^{3} } \\ \\ \implies\frac{51 \times 8}{( {( {5}^{3} \times 2}^{3} ))} = \frac{428}{ {(10)}^{3} } \\ \\ \implies \frac{428}{1000} = 0.428$


Clearly, it is representing terminating decimal.


Proved!!

Answer 2

$\frac{51}{125} = \frac{51}{ {5}^{3} } \frac{51 \times {2}^{3} }{ {5}^{3} \times {2}^{3} } \\ \\ => \frac{51 \times 8}{( {( {5}^{3} \times 2}^{3} ))} = \frac{428}{ {(10)}^{3} } \\ \implies \frac{428}{1000} = 0.428$

here,, it is representing terminating decimals.