Chapter Notes: Percentages

# Chapter Notes: Percentages Notes | Study Mathematics for Class 5 - Class 5

## Document Description: Chapter Notes: Percentages for Class 5 2022 is part of Mathematics for Class 5 preparation. The notes and questions for Chapter Notes: Percentages have been prepared according to the Class 5 exam syllabus. Information about Chapter Notes: Percentages covers topics like Introduction, Money and Metric Measures as Percentages, Finding Percentage of a Number and Chapter Notes: Percentages Example, for Class 5 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Chapter Notes: Percentages.

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Introduction

Per cent means out of hundred. 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 per cent of the whole.
The unshaded part comprises 70 per cent of the whole.

The symbol of per cent 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 denominator can be considered as a per cent.
For example, 15 / 100 means 15%, 60 / 100 means, 60%.
Consider the following example:
In an examination Priya secured 72% marks. What does it mean?
It means she obtained 72 marks out of 100 marks.

Converting a Per cent 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.

Edurev Tips: By a certain per cent we mean that many hundredths.

Converting a Fraction and a Decimal into a Per cent

• To convert a fraction into a per cent, 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 3: Express each of the following as a per cent:
(a) 11 / 20
(b) 14 / 25
(c) 27 / 50

(a)

(b)

(c)

Example 4: 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.
So, 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.
50 cm  = 50% 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.
10 g = 1% 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

Example 5: 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 6: 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 hose Percentage is Given

Example 7: 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.

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