The term “percentage” was adapted from the Latin word “per centum”, which means “by the hundred”. Percentages are fractions with 100 as the denominator.
In other words, it is the relation between part and whole where the value of “whole” is always taken as 100.
This percent symbol (%) can always be replaced with “divided by 100” to convert it into a fraction or decimal equivalent.
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$\text{Percentage} = \left( \frac{\text{Value}}{\text{Total Value}} \right) \times 100$
Conversion Between Percentages and Decimals
- to convert percentages into decimals, just replace % with “divided by 100”. For example, 40% = 40/100 = 0.4.
- to convert decimals into percentages, just multiply by 100. For example, 0.4 = 0.4 × 100 = 40%.
Percentage Changes
Percentage Increase = (Increased Value-Original value)/Original value × 100
Example: The cost of a jacket is increased from $100 to $150. Then by what percentage the price is increased?
Solution: Percentage increase = (150 - 100) / 100 × 100 = 50%.
Percentage Decrease= (Original value-Decreased Value)/Original Value × 100
Example: The amount of rainfall has decreased from 127 mm to 103 mm. Then what is the corresponding percentage decrease?
Solution: Percentage decrease = (127 - 103) / 127 × 100 = 18.9% (Approximately).
- Percentages are reversible. For example, 50% of 60 is the same as 60% of 50.
Profit & Loss
==Profit== = ==Selling Price== ==-== ==Cost Price==
==Loss== = ==Cost Price== - ==Selling Price==
Profit Percentage= (Profit/Cost Price) *100
Loss Percentage= (Loss/Cost Price)*100