Percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, "%". For example, 45% (read as "forty-five percent") is equal to 45 / 100, or 0.45.
Percentages are correctly used to express fractions of the total. For example, 25% means 25 / 100, or one quarter, of some total.
The fundamental concept to remember when performing calculations with percentages is that the percent symbol can be treated as being equivalent to the pure number constant 1 / 100 = 0.01. , for an example 35% of 300 can be written as (35 / 100) × 300 = 105.
To find the percentage of a single unit in a whole of N units, divide 100% by N. For instance, if you have 1250 apples, and you want to find out what percentage of these 1250 apples a single apple represents, 100% / 1250 = (100 / 1250)% provides the answer of 0.08%.
To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:
- (50 / 100) × (40 / 100) = 0.50 × 0.40 = 0.20 = 20 / 100 = 20%.
It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% = 25 / 100 = 0.25, not 25% / 100, which actually is (25 / 100) / 100 = 0.0025.)
Percent of change (percent of increase or percent of decrease) can be calculated using the following formula:
Percentage of change = (Change in quantity/original quantity) * 100
Examples
1. What is 200% of 30?
Answer: 200% × 30 = (200 / 100) × 30 = 60.
2. 60% of all university students are male. There are 2400 male students. How many students are in the university?
Answer: 2400 = 60% × X, therefore X = (2400 / (60 / 100)) = 4000.
3. Denis's car insurance premium for last year was $1440. If she paid $1512 this year, what is the percent of increase on her car insurance premium?
Answer:($1512-$1440)/$1440 — 100% = 72/1440 — 100% = 5% Hence, the percent of increase on the car insurance premium is 5%.
Assignment
1. The price of a Maruti car rises by 30% while the sales of the car came down by 20%. What is the percent change in the total revenue?
2. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what I had paid. What percent of the total amount paid by me was paid for the pens?
