Question

How do you convert $\dfrac{1}{5}$ to a decimal?

Answer 1

Hint:
It is always better to look at the denominator first when we need to convert a fraction into decimal. If the denominator only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in a power of 10 and the result will be a limiting decimal. In case it has a prime factor other than $2$ and $5$, conversion to decimal could be longer and will result in an infinite loop with repeating decimals.

Complete Step by Step Solution:
According to given information, we need to convert $\dfrac{1}{5}$ into decimal.
As the only prime factor of the denominator which is $5$is $5$.
In fact, $5$is a prime number itself, i.e., $(5) = 5$.
Further, we can convert the fraction $\dfrac{1}{5}$ by multiplying numerator and denominator by $2$into $10$, which is a power of $10$.
 Hence,
 \[\dfrac{1}{5} = \dfrac{{1 \times 2}}{{5 \times 2}} = \dfrac{2}{{10}} = 0.2\]
Therefore, we get that $\dfrac{1}{5}$ can be written as $0.2$ in a decimal form.

We finally get $\dfrac{1}{5} = 0.2$.

Additional Information:
A fraction is made up of two parts: a numerator and a denominator. It represents how many parts we have out of the total number of parts. So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.

Note:
It is always better to look at the denominator first when we need to convert a fraction into decimal. If a denominator only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in a power of $10$ . This is always possible if only prime factors of denominator are 2's and 5's - just multiply by as many 5's and 2's.