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Calculate Percentages. Convert to Fractions and Decimals

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.

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.
= 40 100 = 2 5


Example 2: Convert 53% into fraction.
= 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 18 100 into percentage.
18 100 = 18%


Example 2: Convert fraction 45 100 into percentage.
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 3 5 into percentage.
= 3 5 × 100 = 300 5 = 60%


Example 2: Convert fraction 3 1 2 into percentage.
= 7 2 × 100 = 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 3 5 into percentage.
= 3 5 × 20 20 = 60 100 = 60%


Example 2: Express fraction 3 1 2 into percentage.
3 1 2 = 7 2
= 7 2 × 50 50 = 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.
= 15 100 × 100 = 15.00 = 15%


Example 2: Convert 1.123 into percentage.
= 1123 1000 × 100 = 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% = 15 100 = 0.15


Example 2: Convert 1.123 into decimals.
1.123% = 1.123 100 = 1123 100 × 1000 = 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% = 10 100
Step 2: Multiply it by total amount of quantity, which is 25kg.
10 100 × 25 = 25 10
= 2.5 kg


Example 2: 5 1 2 % of 160 litres.
= 11 2 % of 160 litres
= 11 2 × 100 × 160
= 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
50 5000 × 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
60 500 × 100 = 12%

Note

Always keep units of both quantities the same while calculating what percent a one quantity is of another quantity.

Multiple Choice Questions

1) Decimal form of 86% is

  1. 0.86
  2. 8.6
  3. 0.086
  4. 86.00

2) Correct fractional number of 0.15 is

  1. 5 20
  2. 6 20
  3. 3 20
  4. 15 10

3) Correct form of 1 2 5 as percentage

  1. 70%
  2. 60%
  3. 140%
  4. 7%

4) Choose correct percentage form of fractional number 36 100

  1. 36%
  2. 50%
  3. 63%
  4. 18%

5) Correct decimal form of 6.7% is

  1. 6.7
  2. 0.67
  3. 0.067
  4. 67.0

6) 40% of 250cm is

  1. 25cm
  2. 40cm
  3. 100cm
  4. 250cm

7) What percent is 24 hours of 4 days.

  1. 25%
  2. 24%
  3. 50%
  4. 75%

8) What percent a student scored in a test, if he gets 380 out of 400

  1. 38%
  2. 40%
  3. 95%
  4. 100%

9) 1% of 1000 is

  1. 100
  2. 1000
  3. 1
  4. 10

10) If 12% of apples are rotten out of 200 good apples. The number of rotten apples are

  1. 24
  2. 200
  3. 12
  4. 42

Worksheet

1) Express the following percentage as a fraction.

a) 60%

b) 100%

c) 1%

d) 7 1 2 %

e) 0.12%

2) Express the following fraction as percentage.

a) 3 4

b) 9 5

c) 1 3 10

d) 7 25

e) 21 20

3) Express the following percentage as decimals.

a) 12%

b) 0.21%

c) 33%

d) 99.9%

e) 7.4%

4) Express the following decimal as percentage.

a) 0.12

b) 4.053

c) 0.23

d) 1.999

e) 0.01