Percentage
What is Percentage?
A number or ratio expressed as a fraction of 100. It is denoted by the symbol '%'.
Key formula / rule: Percentage Calculation
Key points
- Understand the concept of percentage and its representation.
- Convert between percentages, fractions, and decimals.
- Calculate percentage increase and decrease.
- Solve problems involving successive percentage changes.
Common exam trap
Calculating percentage increase/decrease on the wrong base value.
Definitions
- Term
Percentage
- Meaning
A number or ratio expressed as a fraction of 100. It is denoted by the symbol '%'.
- Term
Percentage Point
- Meaning
A unit of percentage. For example, an increase from 10% to 12% is an increase of 2 percentage points.
- Term
Successive Percentage Change
- Meaning
A series of percentage changes applied one after another to a base value, where each subsequent change is calculated on the result of the previous change.
Learning objectives
Understand the concept of percentage and its representation.
Convert between percentages, fractions, and decimals.
Calculate percentage increase and decrease.
Solve problems involving successive percentage changes.
Apply percentage concepts to real-world scenarios and word problems.
Formulae
- Name
Percentage Calculation
- Note
Used to find the percentage value of a given part with respect to a whole.
- Expression
Percentage = (Part / Whole) * 100
- Name
Percentage Increase
- Note
Measures the relative increase in a quantity.
- Expression
Percentage Increase = ((New Value - Original Value) / Original Value) * 100
- Name
Percentage Decrease
- Note
Measures the relative decrease in a quantity.
- Expression
Percentage Decrease = ((Original Value - New Value) / Original Value) * 100
- Name
Value after Percentage Increase
- Note
Directly calculates the value after an increase.
- Expression
New Value = Original Value * (1 + Percentage Increase / 100)
- Name
Value after Percentage Decrease
- Note
Directly calculates the value after a decrease.
- Expression
New Value = Original Value * (1 - Percentage Decrease / 100)
- Name
Successive Percentage Change (Two Changes)
- Note
Where x and y are the successive percentage changes (positive for increase, negative for decrease). This formula is an approximation for small percentages; the multiplicative method is more accurate for all cases.
- Expression
Net Percentage Change = x + y + (xy / 100)
- Name
Successive Percentage Change (Multiplicative Method)
- Note
This is the most accurate method for successive changes.
- Expression
Final Value = Initial Value * (1 ± x/100) * (1 ± y/100) * ...
Prerequisites
Basic arithmetic operations (addition, subtraction, multiplication, division).
Understanding of fractions and decimals.
Basic algebra (solving simple equations).
Common mistakes
Calculating percentage increase/decrease on the wrong base value.
Incorrectly applying successive percentage changes (e.g., adding percentages instead of multiplying factors).
Confusing percentage points with percentage change.
Errors in converting percentages to fractions or decimals and vice-versa.
Keywords
Percentage
Percent
Ratio
Fraction
Decimal
Increase
Decrease
Profit
Loss
Interest
Discount
Successive Change
Practice preview
Express the fraction 3/8 as a percentage.…
easy
The price of an item is first increased by 10% and then decreased by 10%. What is the net percentage change in the price?…
medium
If a number is increased by 20%, and the original number was 80, what is the new number?…
easy