Percentage

What is Percentage?

Percentage comes from the Latin word “Percentum,” meaning “per hundred.” A percentage represents a part of 100. It is similar to a fraction and is denoted by the symbol %. For instance, if 12 out of 100 students are absent, we say 12% of the students were absent. Any fraction with a denominator of 100 can be expressed as a percentage.

Examples:

• 70/100 = 70%
• 20/100 = 20%
• 53/100 = 53%
• 97/100 = 97%

Formula to Calculate Percentage

To find the percentage when the total is not 100, you use the formula:

Percentage=( Part / Total )×100

Example: If there are 60 students and 3 are absent, the percentage of absent students is:
Percentage=( 3 / 60 )×100=5%

Using Percentage to Compare Quantities

Percentage is a useful tool for comparing quantities. For instance, if Yusra scores 80 out of 120 in Maths and Tasnim scores 70 out of 100, it’s hard to tell who did better just by looking at the scores. Using percentages makes it clearer:

Yusra’s percentage: ( 80 / 120 )×100=66.6%
Tasnim’s percentage: ( 70 / 100 )×100=70%
Since 70% is higher than 66.6%, Tasnim scored better.

How to Calculate the Percentage of Marks

To find the percentage of marks for students who failed:

• Student A: ( 15 / 80 )×100=18.75%
• Student B: ( 30 / 80 )×100=37.5%
• Student C: ( 22 / 80 )×100=27.5%
• Student D: ( 7 / 80 )×100=8.75%
• Student E: ( 35 / 80 )×100=43.75%

If 5 out of 30 students failed, the percentage of students who failed is:
( 5 / 30 )×100=16.66%

Important Conversions

To convert to a percentage:

• 1/5 = ( 1 / 5 )×100=20%
• 0.6 = ( 6 / 10 )×100=60%
• 2:8 = ( 2 / 8 )×100=25%
• 9 = 9×100=900%

To convert 20% into:

• Fraction:  20 / 100 = 1 / 5
• Decimal: 20 / 100 =0.2
• Ratio: 20 / 100 =1:5

Percentage Increase and Decrease

Percentage change is calculated based on the initial value. For example, a 10% discount on a Rs 1000 t-shirt reduces the price by Rs 100, making the final price Rs 900.

Decrease Percentage

• Initial Value > Final Value
• Decreased Value = Initial Value – Final Value
• Decreased Value = x% of Initial Value

Increase Percentage

• Initial Value < Final Value
• Increased Value = Final Value – Initial Value
• Increased Value = x% of Initial Value

Examples of Percentage Change

Example 1: Student Increase
If the number of students increased from 1000 to 1500:

• Increase = 1500 – 1000 = 500
• Percentage Increase = ( 500 / 1000 )×100=50%

Example 2: Work Hours Change
If Nupur worked 45 hours in November and 65.5 hours in December:

• Increase = 65.5 – 45 = 20.5
• Percentage Increase = ( 20.5 / 45 )×100=45.5%

If Nupur worked 45 hours again in January:

• Decrease = 65.5 – 45 = 20.5
• Percentage Decrease = ( 20.5 / 65.5 )×100=31.2%

Understanding and calculating percentages helps in comparing quantities, understanding discounts, and analyzing data effectively.

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