What are Decimals?
Decimals are quantities that are created from fractions. Representing all fractions in the usual form of \(\frac{⬜}{⬜}\) is not always suitable. In such cases, decimals help us represent fractions and mixed numbers in an easy-to-use form.
Some examples of decimals are:
1.5, 3.4, 5.25, and other numbers that look like this.
Why do we need Decimals?
Decimals are used to perform complex calculations where whole number calculations cannot solve the purpose. Decimals are also used to represent fractions and mixed numbers to ease out the process of calculations. A decimal number has two parts; the digits before the decimal point represent the whole part and the digits after the decimal point represent the fractional part.
For example:
In the number 1.5,
1 is a whole part and .5 (or \(\frac{1}{2}\)) represents a fraction.
1.5 is actually \(1\frac{1}{2}\).
Percents as Decimals
Percentages or percents, in the simplest terms, are representations of any number or ratio that can be written as a fraction with a denominator of 100. Now to understand the conversion of a percent value to decimal, let us consider a grid as shown below:
Now consider we want to write 32% as a decimal.
32% denotes 32 equal parts out of 100.
This can be seen below:
We saw that 32% denoted 32 equal parts out of 100 equal parts and this can also be written as \(\frac{32}{100}\). We also know that division by 100 shifts the decimal two places to the left.
So, 32% can be easily converted to decimals by moving the decimal place two places to the left which is initially after 32.
Let us solve some examples to understand this better:
Write the following percents as decimals and use a model to represent them:
- 42%
- 63.5%
Solution :
1. 42%
To convert the above fraction to decimals, first remove the percent(%)symbol. Then divide it by 100 to move the decimal two places to the left.
This can also be seen as a model:
2. 63.5%
To convert the above fraction to decimals first remove the percent(%)symbol. Then divide it by 100 to move the decimal two places to the left.
This can also be seen as a model as follows :
This was how to convert a percent to a decimal. Now let us figure out how to convert decimals to percentages.
Decimals as Percents
To convert a decimal to a percentage we follow a two-step process:
Step 1: Multiply by 100 and move the decimal two places to the right.
Step 2: Add a percent symbol(%) to the final answer.
Let us solve some examples to understand this better:
Write the following decimals as percentages and represent them using a grid model:
- 0.74
- 0.663
Solution:
1. 0.74
Multiply by 100 and move the decimal two places to the right, and add a percent symbol(%).
2. 0.663
Multiply by 100 and move the decimal two places to the right, and add a percent symbol(%).
Conversion of percentages to decimals and vice versa now will be a cakewalk. There is one more conversion left to learn and that would sum it all up.
Fractions as Decimals and Percentages
Let us understand this by converting \(\frac{21}{25}\) to decimal and percentage.
To convert \(\frac{21}{25}\) to the percentage we know that we need to make the denominator 100.
This can be done by using the concept of equivalent fractions.
\(\frac{21}{25}=\frac{21 \times\ 4}{25\ \times 4}\)
\(=\frac{84}{100}\)
Clearly, this can be written as :
Hundredths place is the second place after the decimal point (or to the right )and its value can be obtained as shown
In \(\_\_\_\_\_.\_\_\_ ⬜\_\_\_\longrightarrow \) place value of ⬜is \(=\frac{⬜}{100}\)
Or,
In 3.142 the 4 is the hundredth place and has the place value of \(\frac{4}{100}\).
This is different from the hundreds place as that is taken before the decimal point (or to the left) and has a place value in multiples of 100.
For example; in 653.142 the hundreds place is 5 and its place value is 500 .
% represents percentage. Percentage is nothing but a way of representation of any number or ratio that can be written as a fraction with denominator 100.
100% signifies an entity which is a whole. For example a whole pizza is 100% or if you score full marks in an exam then that is 100%. 100% can also be written as 100 out of 100 or \(\frac{100}{100}\) which is 1 or 1.0