Percentages Class 5 Notes Maths

Did you know that 'percent' means 'per hundred'? 
Imagine splitting anything into 100 equal parts—a chocolate bar, a pizza, or a test score. 

In this Chapter, we’ll learn how percentages make comparing things easier. Get ready to unlock the power of 100.

Introduction

• Per means out of and cent means 1 hundred. Therefore, per cent means out of 1 hundred.
• In the figure, a square is divided into 100 equal parts. Out of the 100 small squares, 30 squares are shaded. 
• The shaded part comprises 30 out of 100 or 30 percent of the whole.
• The unshaded part comprises 70 per cent of the whole.
  
• The symbol of percent is %.
• So, 7% means 7 out of 1 hundred = 7 / 100.
  20% means 20 out of 1 hundred = 20 / 100.
  80% means, 80 out of 1 hundred = 80 / 100.
• We note that a fraction with 100 as the denominator can be considered as a per cent.
  For example, 15 / 100 means 15% , 60 / 100 means, 60%.
• In an examination, Priya secured 72% marks. What does it mean?
  It means she obtained 72 marks out of 100 marks.

Converting a Percentage into a Fraction or a Decimal

• To convert a per cent into a fraction, drop the per cent sign and divide the remaining number by 100. Express the fraction so obtained in its lowest terms.
• To convert a per cent into a decimal, first change it into a fraction with denominator as 100 and then shift the decimal point to the left by two places.

Example 1: Express each of the following per cents as a fraction:
(a) 15%
(b) 64%
(c) 95%

(a) 15% = 15 / 100 = 3 / 20
(b) 64% = 64 / 100 = 16 / 25
(c) 95% = 95 / 100 = 19 / 20

Example 2: Express each of the following per cents as a decimal.
(a) 11%
(b) 72%
(c) 85%

(a) 11% = 11 / 100 = 0.11
(b) 72% = 72 / 100 = 0.72
(c) 85% = 85 / 100 = 0.85

Converting a Fraction and a Decimal into a Percentage

• To convert a fraction into a percentage, multiply the given fraction by 100 and write the symbol %.
• To convert a decimal into a per cent, multiply the given decimal by 100 and write the symbol %.

Example 1: Express each of the following as a percentage: 
(a) 11 / 20
(b) 14 / 25
(c) 27 / 50

(a)

(b)

(c)

Example 2: Express each of the following as a per cent:
(a) 0.14
(b) 0.35
(c) 0.75

(a) 0.14 = (0.14 × 100)% = 14%.
(b) 0.35 = (0.35 × 100)% = 35%.
(c) 0.75 = (0.75 × 100)% = 75%.

Money and Metric Measures as Percentages

1. We know that, 100 paise = 1 rupee.
   1 paisa = 1 / 100 of a rupee. 
   1 paisa = 1% of a rupee.
   Similarly, 2 paise = 2% of a rupee.
   10 paise = 10% of a rupee.  
   75 paise = 75% of a rupee.
2. We know that, 100 cm = 1 metre
   So, 1 cm = 1 / 100 of a metre. 
   1 cm = 1% of a metre.
   2 cm = 2% of a metre.  
   20 cm = 20% of a metre.
3. We know that, 1,000 g = 1 kg
   
   1 g  = 0.1% of a kg. 
   2 g = 0.2% of a kg.
   15 g = 1.5% of a kg
   100 g = 10% of a kg. 
   500 g = 50% of a kg.
4. We know that, 1,000 ml = 1l
   
   1 ml = 0.1% of a l.  
   3 ml = 0.3% of a l.
   10 ml = 1% of a l.  
   250 ml = 25% of a l.

Finding Percentage of a Number

The following examples will help you to understand the required procedure.

Example 1: Find: 
(a) 20% of 80 
(b) 32% of 75 
(c) 45% of 80 days

(a) 20% of 80

Hence, 20% of 80 = 16.
(b) 32% of 75

Hence, 32% of 75 = 24
(c) 45% of 80 days

Hence, 45% of 80 days = 36 days.

Example 2: What per cent of 80 is 60?

60 out of 80 is equivalent to the fraction 60 / 80.

Hence, 75% of 80 is 60.

To Find the Number whose Percentage is Given

Example : Find the number whose:
(a) 15% is 24
(b) 36% is 117

(a) We have, 15% of the required number = 24

Thus, the required number

Hence, 160 is the required number whose 15% is 24.
(b) We have 36% of the required number = 117

Thus, the required number

Hence, 325 is the required number whose 36% is 117.