Question

How do you find the decimal notation of a percent?

Answer 1

Hint: The percentage in mathematics is a ratio or proportion or share of an object concerning a whole body. The percentage is always written concerning $100\% $ . Decimal is a fraction whose denominator is always a power of $\;10$ and the numerator is the value we want to express as a decimal.

Complete step-by-step answer:
The word ‘percent’ means per hundred
Hence the percentage is used to express a proportion of something concerning the whole body, where the whole body is considered as a hundred percent or $100\% $ .
For example, consider a glass half-filled with water. We want to find the percentage of water in the glass.
Here, the glass is the whole body and water is the object, whose percentage we want to find.
Hence, the glass is considered as $100\% $ .
Now, the glass is half-filled with water. Hence to express as a percentage, we can say there is half of $100\% $ in the glass
$ \Rightarrow 100 \times \dfrac{1}{2} = 50$
Hence we conclude from here that there is $50\% $ water in the glass or the glass is $50\% $ filled with water.
Hence in percentage, if the whole body is filled with the object we say it as $100\% $ and if the whole body is empty, we can say it as $0\% $ .
In the decimal, we write the whole part of a number on the left-hand side and the fractional part on the right-hand side of the point, which is known as the decimal point.
To convert a percentage value into a decimal, we divide the percentage value by $\;100$ and remove the percentage sign.
This happens because in percentage we write the whole body as $100\% $ , while in decimal we write the whole body as $\;1$ on the left-hand side of the decimal point. Hence we get to decimal from percent by dividing the percent by $\;100$ .
For example, we want to express $75\% $ as a decimal
Hence, dividing it by $\;100$ we get,
$ \Rightarrow \dfrac{{75}}{{100}} = 0.75$
We know that the value of the percentage lies between $\;0$ and $\;100$ .

As by dividing percent by $\;100$ , we get the decimal value, we can say that decimal value lies between $\;0$ and $\;1$.

Note:
As the value of percentage is always positive, the value of decimal is also always positive. For a short method to convert percent to decimal, we have to shift the decimal point two places to the left. For example, for $75.36\% $ the decimal is $\;0.7536$ . For percent $8.25\% $ , the decimal value is $\;0.0825$.