Question

How do you convert:- \[\left( { - \dfrac{1}{8}} \right)\] into a percent and decimal ?

Answer 1

Hint: In the given question, we are required to convert a given fraction into decimal and percent. The fraction is having numerator and denominator. So, we first simplify the fraction and bring it in simplest form. Then, we convert it into percentage by multiplying it with $ 100 $ and in order to convert it in decimal we will perform the division. The fraction may also be converted into decimal directly by division.

Complete step by step solution:
The given question requires us to convert the given fraction into its simplest form by cancelling out the common factors in numerator and denominator and then expressing it as decimal representation and percent.
So, to convert the given fraction into its simplest form, we factorise the numerator as well as denominator and look for the common factors.
We have, the numerator of the fraction is $ 1 $ and the denominator is $ 8 = 2 \times 2 \times 2 $ .
So, the fraction is already in simplest terms. Hence, we multiply the numerator and denominator by $ 12.5 $ so as to get $ 100 $ in the denominator.
So, we get,
\[\left( { - \dfrac{1}{8}} \right) \times \left( {\dfrac{{12.5}}{{12.5}}} \right) = \left( { - \dfrac{{12.5}}{{100}}} \right)\]
Percent means how many parts in a hundred. So, the fraction \[\left( { - \dfrac{1}{8}} \right)\]is the same as $ - 12.5\% $ .
Now, to convert the fraction into the decimal representation, we divide the numerator by the denominator until we get zero as the remainder. We know that when dividing by \[100\], we can just simply move the decimal point to the left side by two places. So, we get,
Hence, we get, \[\left( { - \dfrac{1}{8}} \right) = - \dfrac{{12.5}}{{100}} = - 0.125\].
Therefore, the fraction \[\left( { - \dfrac{1}{8}} \right)\] can be represented as $ - 0.125 $ in decimal form and $ - 12.5\% $ in percent form.

Note: The division of the numerator by the denominator can be a cumbersome task as it involves thorough knowledge of algebraic rules and long division method. Care should be taken while doing the same and proceeding with the process to convert a fraction into decimal.