Question

How do you convert $ \left( {\dfrac{3}{{10}}} \right) $ as a decimal and a percent?

Answer 1

Hint: In the given question, we are required to convert a given fraction into decimal and percent. The fraction has a numerator and denominator. So, we first simplify the fraction and bring it in simplest form. Then, we convert it into a 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 decimal and percent. We first have to convert the fraction into its simplest form by cancelling out the common factors in numerator and denominator and then expressing it as a decimal representation.
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, $ 3 = 3 \times 1 $ and $ 10 = 5 \times 2 $ .
So, we notice that there is no common factor in the numerator and the denominator. So, we keep the fraction unchanged.
Now, to convert this fraction into percentage, we have to make the denominator $ 100 $ by multiplying the numerator and denominator by the same number so as not to change the fraction.
So, we multiply the numerator and denominator by $ 10 $ in order to get $ 100 $ in the denominator.
Hence, we get,
So, to make the denominator equal to $ 100 $ , we have to multiply both the numerator and denominator by $ 12.5 $ . So, we get,
 $ \Rightarrow \left( {\dfrac{3}{{10}}} \right) \times \left( {\dfrac{{10}}{{10}}} \right) = \left( {\dfrac{{30}}{{100}}} \right) $
So, the fraction $ \left( {\dfrac{3}{{10}}} \right) $ can be represented as $ 30\% $ in percentage.
Now, to convert the fraction into the decimal representation, we divide the numerator by the denominator until we get zero as the remainder.
Hence, we get, $ \left( {\dfrac{3}{{10}}} \right) = 0.30 $ .
Therefore, we can represent the fraction $ \left( {\dfrac{3}{{10}}} \right) $ in decimal as $ 0.3 $ and in percentage as $ 30\% $ .

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.