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How to Calculate Percentage?

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In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we want to calculate the percent of a number out of a given number then we have to divide the number by the given number and multiply the result by 100. Hence, the percentage means a part per hundred. The word percent means per out of 100. It is represented by the symbol “%”.

Examples of percentages are: 

10% is equivalent to 1/10 fraction
20% is equivalent to ⅕ fraction
25% is equivalent to ¼ fraction
50% is equivalent to ½ fraction
75% is equivalent to ¾ fraction
90% is equivalent to 9/10 fraction

Percentages have no dimension. Hence it is a dimensionless number. If we say 50% of a number, it means 50 percent of its whole.

Percentages can also be represented in decimal or fraction form, such as 0.6%, 0.25%, etc. In academics, the marks obtained in any subject are calculated in terms of percentage

There are many formulas for calculating percentage problems. but we can think of the most basic as 

P% = (X/Y)×100

where,

X is the number obtained,

Y is the number out of which we have to calculate the percentage.

Question: How to calculate the percentage of a number, as what is 5% of 150?

Answer:

Convert the given problem into an equation using the percentage formula as follows:

5% of 150 = 5/100 × 150

                 = 750/100

                 = 7.5

So 5% of 150 is 7.5

Fraction to Percentage

We will follow the following steps for converting a decimal into a percentage:

  • Get the number in fraction form.
  • Then we need to multiply the fraction by 100
  • Add the percent symbol after the product.

Percentage = Fraction × 100

Question: Change the given fractions into percentages.

  1. Express 11/20 as a percent.
  2. Express 2/4 as a percent.
  3. Express 30/5 as a percent.
  4. Express 10/2 as a percent.
  5. Express 19/4 as a percent.
  6. Express 27/2 as a percent.

Answer:

1. Express 11/20 as a percent.

Let us consider how to change a fraction to a percentage

11/20 = 11/20 × 100 %

          = 1100/20 %

          = 55 %

2. Express 2/4 as a percent.

Let us consider how to change a fraction to a percentage

2/4 = 2/4 × 100 %

       = (2 × 100)/4 %

       = 200/4 %

       = 50%.

3. Express 30/5 as a percent.

Let us consider how to change a fraction to a percentage

30/5 = 30/5 × 100 %

        = (30 × 100)/5 %

        = 3000/5 %

        = 600%.

4. Express 10/2 as a percent.

Let us consider how to change a fraction to a percentage

10/2 = 10/2 × 100 %

        = (10 × 100)/2 %

        = 1000/2 %

       = 500%

5. Express 19/4 as a percent.

Let us consider how to change a fraction to a percentage

19/4 = 19/4 × 100%

        = (19 × 100)/4 %

        = 1900/4 %

        = 475%.

6. Express 27/2 as a percent.

Let us consider how to change a fraction to a percentage

27/2 = 27/2 × 100 %

        = (27 × 100)/2 %

        = 2700/2 %

        = 1350%.

Ratio to Percentage and vice versa

Ratios are often expressed in the form 

m:n or m/n.

To convert a ratio into the form of a percentage, simply divide m by n and then multiply the result by 100.

The ratio to percentage formula is used to convert the ratio to percentage. The ratio to percentage formula is given as follows:

Percentage = Ratio × 100

Question: Change ratios into percentages

  1. Convert the ratio 3:1 to percentage.
  2. Convert 75% into a ratio.
  3. What is 25% as a ratio?
  4. Convert 45% into the ratio.
  5. What is 55% as a ratio?
  6. Convert the ratio 2:1 to percentage.

Answer:

1. Convert the ratio 3:1 to percentage.

The percentage value of 4:1 is calculated as follows:

3:1 = (3/1) ×100 

      = 300%

Thus, the percentage of the ratio of 3:1 is 300% 

2. Convert 75% into a ratio.

75% 

= 75/100

= 3/4

Therefore, 75% = 3: 4

3. What is 25% as a ratio?

25% 

= 25/100 

= ¼.

Therefore, the ratio equivalent to 25% is 1:4

4. Convert 45% into the ratio.

45% 

= 45/100 

= 9/20

Therefore, 45% = 9:20

5. What is 55% as a ratio?

55% 

= 55/100 

= 11/20

Therefore, the ratio equivalent to 55% is 11/20.

6.Convert the ratio 2:1 to percentage.

The percentage value of 2:1 is calculated as follows

2:1 

= (2/1) ×100 

= 200%

Thus, the percentage of the ratio of 2:1 is 200%

Decimal into a Percentage

We will follow the following steps for converting a decimal into a percentage:

Obtain the number in decimal form. Multiply the number in decimal form by 100 and put the percent sign (%)

Note: When we multiply the decimal number by 100, then we need to shift the decimal point two places to the right

Question: Change decimals into percentages

Answer: 

Conversion of decimal into percentage

(i) 0.29 = 0.29 × 100 % = 29 %

(ii) 0.25 = 0.25 × 100 % = 25 %

(iii) 0.01 = 0.01 × 100 % = 1 %

(iv) 0.51 = 0.51 × 100 % = 51 %

(v) 13.01 = 13.01 × 100 % = 1301 %

(vi) 201.17 = 201.17 × 100 % = 20117 %

(vii) 100.11 = 100.11 × 100 % = 10011 %

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Last Updated : 10 Aug, 2022
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