Question

How do you convert $0.5\%$ into a fraction and decimal?

Answer 1

Hint: In this question we have been given a number which is in the percentage form which we have to convert into a fraction and a decimal. To convert the number into a fraction, we will eliminate the percentage from the number by dividing it with $100$ and then we will eliminate the decimal from the numerator by multiplying the number such that we get an appropriate fraction. To get the decimal value we will divide the numerator by the denominator.

Complete step by step solution:
We have the number given to us as:
$\Rightarrow 0.5\%$
It can be seen that the number has a $\%$ sign. This means that the number is in the form of a percentage. Percentage means a number per century, which means a number divided by $100$ therefore, we can write the number as:
$\Rightarrow \dfrac{0.5}{100}\to \left( 1 \right)$
Now we have a decimal number in the numerator therefore to remove the numerator, we will multiply the numerator and denominator by $10$.
On multiplying, we get:
$\Rightarrow \dfrac{0.5\times 10}{100\times 10}$
On simplifying, we get:
$\Rightarrow \dfrac{5}{1000}$
On simplifying, we get:
$\Rightarrow \dfrac{1}{200}$, which is required fraction form.
Now to find the decimal value, we will consider equation $\left( 1 \right)$
$\Rightarrow \dfrac{0.5}{100}$
Since there are $2$ tens places in the denominator, we will put two additional decimals in the denominator to remove it.
Therefore, it can be written as:
$0.005$, which is the required decimal form.

Note: In this question we can see that the fraction of the number is in the form of a proper fraction which has the denominator greater than the numerator. The percentage of a value can be calculated by using the formula $\dfrac{a}{b}\times 100$ where $a$ is part of the quantity and $b$ is the value of total quantity.