Question

Without performing actual division find what type of decimal representation the following have. (i). 39/1300 (ii). 64/910

Answer 1

Answer: lowest term of 39/1300=3/100

Prime factors of hundred=2x2x5x5

So,it is a terminating representation because as we know a number is terminating if it's factors are 2 or 5 and both 2 and 5

Answer 2

i) $\dfrac{39}{1300}$ is terminating.

ii) $\dfrac{64}{910}$ is non-terminating.

Step-by-step explanation:

To find : Without performing actual division find what type of decimal representation the following have ?

Solution :

When the denominator of the fraction is in form of $2^m\times 5^n$ then the given decimal is terminating and if it is not then it is non-terminating.

So we factories the denominator into the form,

i) $\frac{39}{1300}$

$\frac{39}{1300}=\frac{39}{2\times2\times 5\times 5\times 13}$

$\frac{39}{1300}=\frac{3}{2^2\times 5^2}$

It is in the form so the decimal is terminating.

$\frac{39}{1300}=\frac{3}{10^2}$

$\frac{39}{1300}=0.03$

ii) $\frac{64}{910}$

$\frac{64}{910}=\frac{64}{2\times5\times 7\times 13}$

It is not in the form so the decimal is non-terminating.

$\frac{64}{910}=0.070329670329..$

#Learn more

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