How To Calculate And Convert Percentages To Decimals?

Definition

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.

Real life example

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.

Example of percentages

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 a total of 100 boxes and 70 boxes are shaded which represents the 70% scored marks.

Pictorial representation of 70% in a grid of 10 x 10

Calculate percentage of a number

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 a fractional number and then multiply it by the total amount of quantity.

Examples of finding percentage of number

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.

$\frac{10}{100} \times 25$

= $\frac{25}{10}$

= 2.5kg

$5 \frac{1}{2} %$ of 160 litres.

= $\frac{11}{2} %$ of 160 litres

= $\frac{11}{2 \times 100} \times 160$

= $\frac{11}{20} \times 16$

= $\frac{11}{5} \times 4$

= $\frac{44}{5}$

= 8.8 litres

What percentage of a number is

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.

Examples of what percentage of number

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 5 litre.

Step 1: Divide the one number by another number

$\frac{50}{5000} \times 100$

= 1%

Calculate what percentage 60cm is of 5m.

1 meter = 100 cm

5 meter = 5 × 100 = 500cm

To calculate what percent of 60cm is 5 metre or 500cm.

Step 1: divide the one number by another number

$\frac{60}{500} \times 100$

= 12%

Note

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

Convert percentage to fraction

Percentage values can be written in fractions. The denominator of its fraction always has 100 and the numerator has the value of the percentage given.

To convert a percentage to fraction, the % symbol is dropped and the number is divided by 100. Also, reduce the fractions to its lowest term.

Example of percentage to fraction

Convert 40% to fraction.

= $\frac{40}{100} = \frac{2}{5}$

Convert 53% to fraction.

= $\frac{53}{100}$

Convert fraction to percentage

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

Examples of fraction with denominator 100 to percentage

Convert fraction $\frac{18}{100}$ to percentage.

$\frac{18}{100}$ = 18%

Convert fraction $\frac{45}{100}$ to percentage.

$\frac{45}{100}$ = 45%

Fractions with denominator not 100

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

Method 1: Multiply with 100

Step 1: Write the fraction and multiply it by 100.

Step 2: Reduce the percentage to its lowest term.

Step 3: Put the % symbol after the value obtained in step 2.

Examples of fractions with denominator other than 100 to percentage

Convert fraction $\frac{3}{5}$ to percentage.

= $\frac{3}{5} \times 100$

= $\frac{300}{5}$

= 60%

Convert fraction $3 \frac{1}{2}$ to percentage.

= $\frac{7}{2} \times 100$

= $\frac{700}{2}$

= 350%

Method 2: Using equivalent fraction

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 to convert fraction to percentage using equivalent fraction

Express fraction $\frac{3}{5}$ v to percentage.

= $\frac{3}{5} \times \frac{20}{20}$

= $\frac{60}{100}$

= 60%

Express fraction $3 \frac{1}{2}$ to percentage.

= $\frac{7}{2}$

= $\frac{7}{2} \times \frac{50}{50}$

= $\frac{350}{100}$

= 350%

Convert decimals to percentage

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

Examples of decimals to percentage

Convert 0.15 to percentage.

= $\frac{15}{100} \times 100$

= 15.00

= 15%

Convert 1.123 to percentage.

= $\frac{1123}{1000} \times 100$

= $\frac{1123}{10}$

= 112.3%

Convert percentage to decimals

To convert percentage to 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.

Examples of percentage to decimals

Convert 15% to decimals.

15% = $\frac{15}{100}$

= 0.15

Convert 1.123 to decimals.

1.123% = $\frac{1.123}{100}$

= $\frac{1123}{100 \times 1000}$

= $\frac{1123}{100000}$

= 0.01123

Questions Worksheets

Total - 2

Worksheet

Convert the following percentages to fractions.
1. 60%
2. 100%
3. 1%
4. $7 \frac{1}{2}$
5. 0.12%
Convert the following fractions to percentages.
1. $\frac{3}{4}$
2. $\frac{9}{5}$
3. $1 \frac{3}{10}$
4. $\frac{7}{25}$
5. $\frac{21}{20}$

Questions PDF worksheet

24.8 KB

Worksheet

Convert the following percentages to decimals.
1. 12%
2. 0.21%
3. 33%
4. 99.9%
5. 7.4%
Convert the following decimals to percentages.
1. 0.12
2. 4.053
3. 0.23
4. 1.999
5. 0.01

Questions PDF worksheet

16.5 KB

Multiple Choice Questions Worksheet

1) Decimal form of 86% is

0.86
8.6
0.086
86.00

2) Correct fractional number of 0.15 is

$\frac{5}{20}$
$\frac{6}{20}$
$\frac{3}{20}$
$\frac{15}{10}$

3) Correct form of

1 \frac{2}{5}

as percentage is

70%
60%
140%
7%

4) Choose correct percentage form of fractional number

\frac{36}{100}

5) Correct decimal form of 6.7% is

6.7
0.67
0.067
67.0

6) 40% of 250 cm is

25 cm
40 cm
100 cm
250 cm

7) What percent is 24 hours of 4 days?

8) What is the percentage of marks a student scored in a test, if he gets 380 marks out of 400?

38%
40%
95%
100%

9) 1% of 1000 is

100
1000
1
10

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

MCQ PDF worksheet

29.5 KB

MCQs Answer Keys