PERCENTAGE LEC.3

Introduction to Percentages
Definition: A percentage is a way to express a fraction or a ratio as a fraction of 100. It is denoted by the symbol "%".
Example: 20% means 20 out of 100, or 20/100.
Key Concepts and Formulas
Percentage Change
Formula:
Percentage Change
=
Change in Value
Original Value
×
100
Percentage Change=
Original Value
Change in Value
​
×100
Use this formula to calculate percentage increase or decrease.
Calculating Percentage
To find what percentage one number is of another:
Percentage
=
(
Part
Whole
)
×
100
Percentage=(
Whole
Part
​
)×100
For example, what percentage is 25 of 50?
(
25
50
)
×
100
=
50
(
50
25
​
)×100=50.
Percentage Increase and Decrease
To increase a number by a percentage:
New Value
=
Original Value
×
(
1
+
Percentage Increase
100
)
New Value=Original Value×(1+
100
Percentage Increase
​
)
To decrease a number by a percentage:
New Value
=
Original Value
×
(
1
−
Percentage Decrease
100
)
New Value=Original Value×(1−
100
Percentage Decrease
​
)
Applications in Interest and Profit
Simple Interest:
Simple Interest
=
𝑃
×
𝑅
×
𝑇
100
Simple Interest=
100
P×R×T
​
Compound Interest:
𝐴
=
𝑃
(
1
+
𝑅
100
)
𝑇
A=P(1+
100
R
​
)
T