 Percentage Change

## Percentage

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent". For example: If 50% of the total number of students in the class are male, that means that 50 out of every 100 students are male. If there are 500 students, then 250 of them are male.
The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1250 apples, first, compute the ratio 50/1250 = 0.04, and then multiply by 100 to obtain 4%. The percent value can also be found by multiplying first, so in this example, the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1250 to give 4%.
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%.
Percentage increase and decrease
Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $200 and the price rises 10% (an increase of$20), the new price will be \$220. Note that this final price is 110% of the initial price (100% + 10% = 110%).
Some other examples of percent changes:
• An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of increase = 200% of initial); in other words, the quantity has doubled.
• An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
• A decrease of 60% means the final amount is 40% of the original (100% – 60% = 40%).
• A decrease of 100% means the final amount is zero (100% – 100% = 0%).
In general, a change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount (equivalently, (1 + 0.01x) times the original amount).
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