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Arithmetic : Percents

Preparation Just what you need to know !

 

Percent, Fraction and Decimal

 

The word 'percent' means 'per hundred' or 'out of 100', and % is the percent sign.
Percent is a way of representing a part of something in terms of hundredths (i.e., 1/100).
For example, 100% = 100 hundredths = 100 × (1/100) = 1 and 75% = 75 hundredths = 75 × (1/100) = ¾.
Percent can be expressed as a fraction (with a denominator of 100) or a decimal.
For example, 29% = 29/100 = 0.29
Percents are often used to compare fractions with equal denominators of 100.

 

To convert a percent to a fraction, drop the percent sign and divide the number by 100.
For example, 80% = 80/100 = 4/5 and 125% = 125/100 = 5/4 = 1¼.
As a more complicated example, consider the following:

133 1

3
% = 133 1

3
÷ 100 = 400

3
× 1

100
= 4

3

Note that it is advisable to convert a mixed number to an improper fraction during calculations.

 

To convert a fraction to a percent, multiply the number by 100 and insert the percent sign.
For example, 3/5 = (300/5)% = 60% and 1/16 = (100/16)% = (25/4)% = 6¼% = 6.25%

 

To convert a percent to a decimal, drop the percent sign and divide the number by 100 (i.e., move the decimal point two places to the left, inserting zeros to the left if necesssary).
For example, 13% = 0.13 and 2% = 0.02


 

To convert a decimal to a percent, multiply the decimal by 100 (i.e., move the decimal point two places to the right) and insert the percent sign.
For example, 0.2576 = 25.76% and 0.002 = 0.2%

 

The following fraction and decimal equivalents of percents are worth noting:
1% = 1/100 = 0.01 ; 2% = 1/50 = 0.02 ; 4% = 1/25 = 0.04 ; 5% = 1/20 = 0.05 ; 10% = 1/10 = 0.1 ;
20% = 1/5 = 0.2 ; 40% = 2/5 = 0.4 ; 60% = 3/5 = 0.6 ; 80% = 4/5 = 0.8 ;
25% = 1/4 = 0.25 ; 50% = 1/2 = 0.5 ; 75% = 3/4 = 0.75 ;
120% = 6/5 = 1.2 ; 125% = 5/4 = 1.25 ; 150% = 3/2 = 1.5 ; 200% = 2

 

Percents greater than 100% may be expressed as numbers greater than 1.
For example, 225% = 225/100 = 2.25
Note that 225% of 60 = 2.25 × 60 = 135

 

Percents less than 1% may be expressed as numbers between 0 and 0.01.
For example, ¼% = 0.25% = 0.0025
Note that ¼% of 8 = 0.0025 × 8 = 0.02

 

MUST-KNOW : When doing calculations with percents, change percents to fractions or decimals.

 

To find a certain percent of a number, multiply the number by the percent expressed as a fraction or decimal.
For example to find 45% of 900, two possible ways are as follows.
Changing percent to fraction gives 45% = 45/100 = 9/20. So, 9/20 × 900 = 405.
Alternatively, changing percent to decimal gives 45% = 45/100 = 0.45. So, 0.45 × 900 = 405.

 

Example
In a school of 350 students, 36% are girls. How many boys are there in the school?
Solution. Percent of boys = 100% − 36% = 64%.
Changing percent to fraction gives 64% = 64/100 = 16/25. So, 16/25 × 350 = 16 × 14 = 224.
Alternatively, changing percent to decimal gives 64% = 64/100 = 0.64. So, 0.64 × 350 = 224.
Therefore, there are 224 boys in the school.

 

Example
A bank has 2100 clients, of whom 378 clients may be classified as high net worth. What percent of the bank clients are high net worth?
Solution. The fraction of clients who are high net worth is 378/2100.
378/2100 = 18/100 (on dividing both numerator and denominator by 21).
18/100 = 0.18 = 18%
Therefore, 18% of the bank clients are high net worth.

 

GMAT Math Review - Arithmetic : Index for Percents
 

GMAT Math Review - Arithmetic : Practice Exercise for Percents

 

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