Question

How do you convert $\dfrac{8}{{10}}$ to a decimal?

Answer 1

Hint:
First, we have to convert the given mixed fraction number to a fractional number. Thereafter, it is always better to look at the denominator first when we need to convert a fraction into a 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.

Complete step by step:
First, we will reduce $\dfrac{8}{{10}}$ to its simplest form.
To do so, we need to divide both the numerator and denominator by 2, as it is a common factor.
Therefore,
\[ \Rightarrow \dfrac{8}{{10}} \div \dfrac{2}{2} = \dfrac{8}{{10}} \times \dfrac{2}{2} = \dfrac{4}{5}\]
So, now we need to turn $\dfrac{4}{5}$ into decimal.
As the only prime factor of the denominator which is $5$is $5$.

In fact, $5$ is itself a prime number.
Further, we can convert the fraction $5$ by multiplying numerator and denominator by $2 \times 2 \times 5$ into $100$, which is a power of $10$.

Hence,

$\dfrac{4}{5} = \dfrac{{4 \times 2 \times 2 \times 5}}{{5 \times 2 \times 2 \times 5}} = \dfrac{{80}}{{100}} = 0.8$

Therefore, we get that $\dfrac{8}{{10}}$ can be written as $0.8$ in a decimal form.

Note:
Decimal notation is a way of writing fractions that have their denominators in the powers of $10$. 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. If the denominator of the given fraction 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.