Percentages, Convert it to Fractions & Decimals

Chapter Contents

What is percentage?
Examples of percentage in real life
Convert percentage into fractions
Convert fractions into percentage
- Fractions with denominator 100
- Fractions with denominator other than 100
Convert decimals into percentage
Convert percentage into decimals
Calculate percentage of a number or quantity
Find what percentage is of a number or a quantity
Worksheet 1
Worksheet 2

What is percentage?

Percentage is a number which is expressed as a fraction with denominator 100.
Percentage is defined from the latin word, which means by a hundred. It means for every 100 or out of hundred. The symbol % is used for percent.

Examples of percentage in real life

Percent can be seen in use in real life while telling the scoring of a student in a subject. It can be seen in expressing the rate of interest that the bank gives on calculating the interest value on a principal amount. Percent can also be seen commonly on any packaging of a food item, where it is written as how many percent are the ingredients that have been used in manufacturing the food item.
Let’s start with an example in detail to understand the percentage topic in maths.

Example

Consider an example of scoring in a subject by a student.
Let’s say a student scores 70% marks in a class test of a math subject.
So, what does 70% marks represent?
70% will be read as 70 percent and it tells that the student scored 70 marks out of one hundred.

70% marks can also be represented pictorially in a grid of 10 x 10. 70 marks are scored out of 100. The grid has total of 100 boxes and 70 boxes are shaded which represents the 70% scored marks.

Convert percentage into fractions

Percentage values can be written in fractions. Denominator of its fraction always has 100 and the numerator has the value of the percentage given.
To convert a percentage into a fraction, the % symbol is dropped and the number is divided by 100. Also, reduce the fractions into its lowest term.

Example

Example 1: Convert 40% into fraction.
$= \frac{40}{100} = \frac{2}{5}$

Example 2: Convert 53% into fraction.
$= \frac{53}{100}$

Convert fractions into percentage

Any fraction can be written into percentage also. The fractions having a denominator of 100 is the simplest fraction that can be changed into percentage easily. The fractions with denominators other than 100 can be converted into percentages with two different methods.

Fractions with denominator 100

If a fraction has denominator of 100, it can be expressed as a percentage by putting 100% symbol after its numerator.

Example

Example 1: Convert fraction $\frac{18}{100}$ into percentage.
$\frac{18}{100} = 18%$

Example 2: Convert fraction $\frac{45}{100}$ into percentage.
$\frac{45}{100} = 45%$

Fractions with denominator other than 100

Such fractions with denominators other than 100 can be converted into percentage by any of the following methods.

Method 1

Step 1: Write the fraction and multiply it by 100.
Step 2: Reduce the percentage into its lowest term.
Step 3: Put the% symbol after the value obtained in step 2.

Example

Example 1: Convert fraction $\frac{3}{5}$ into percentage.
$= \frac{3}{5} \times 100 = \frac{300}{5} = 60%$

Example 2: Convert fraction $3 \frac{1}{2}$ into percentage.
$= \frac{7}{2} \times 100 = \frac{700}{2} = 350%$

Method 2

Step 1: Write the fraction.
Step 2: Convert the fraction to an equivalent fraction with the denominator 100.
Step 3: Put the% symbol after the value obtained in step 2.

Example

Example 1: Express fraction $\frac{3}{5}$ into percentage.
$= \frac{3}{5} \times \frac{20}{20} = \frac{60}{100} = 60%$

Example 2: Express fraction $3 \frac{1}{2}$ into percentage.
$3 \frac{1}{2} = \frac{7}{2}$
$= \frac{7}{2} \times \frac{50}{50} = \frac{350}{100} = 350%$

Convert decimals into percentage

Decimals can be converted into percentages by just multiplying the decimal value with 100 and writing % symbol after the number obtained after multiplication.

Example

Example 1: Convert 0.15 into percentage.
$= \frac{15}{100} \times 100 = 15.00 = 15%$

Example 2: Convert 1.123 into percentage.
$= \frac{1123}{1000} \times 100 = \frac{1123}{10} = 112.3%$

Convert percentage into decimals

To convert percentage into decimals, first of all, the percentage % symbol is removed. Then the number is written as a fraction with the denominator of 100 only. Lastly, this fraction is converted into the decimal form.

Example

Example 1: Convert 15% into decimals.
$15% = \frac{15}{100} = 0.15$

Example 2: Convert 1.123 into decimals.
$1.123% = \frac{1.123}{100} = \frac{1123}{100 × 1000} = \frac{1123}{100000} = 0.01123$

Calculate percentage of a number or quantity

To find the percentage of a number or a quantity, the percent to find out of a quantity is always given. The percent amount of a quantity or a number is calculated out of the total quantity.
To find out the percent amount, write the given percentage in fractional number and then multiply it by total amount of quantity.

Example

Example 1: 10% of 25kg
Step 1: Write the given percentage in fractional number, which is 10%.
$10% = \frac{10}{100}$
Step 2: Multiply it by total amount of quantity, which is 25kg.
$\frac{10}{100} × 25 = \frac{25}{10}$
$= 2.5 kg$

Example 2: $5 \frac{1}{2} %$ of 160 litres.
$= \frac{11}{2} %$ of 160 litres
$= \frac{11}{2 \times 100} \times 160$
$= \frac{44}{5} = 8.8 litres$

Find what percentage is of a number or a quantity

To find what percentage of one number or quantity is of another number or quantity, first divide the number by another number. Then multiply the number obtained by dividing by 100. Put the% symbol after the number obtained after multiplication.

Example

Example 1: Calculate what percentage 50ml is of 5 litre.
1 litre = 1000 ml
5 litre = 5 × 1000 = 5000ml
To calculate what percent of 50 ml is of 5litre.
Step 1: Divide the one number by another number
$\frac{50}{5000} \times 100 = 1%$

Example 2: Calculate what percentage 60cm is of 5m.
1 meter = 100 cm
5 meter = 5 × 100 = 500cm
To calculate what percent of 60cm is of 5 meter or 500cm.
Step 1: divide the one number by another number
$\frac{60}{500} \times 100 = 12%$