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Example:Find Percentage Decrease

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In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in Latin). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. (Our solved example in mathguru.com uses this concept)

Percentages are used to express how large/small one quantity is, relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity, which should be greater than zero. For example, an increase of \($\) 0.15 on a price of \($\) 2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is therefore a 6% increase.


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 constant1 / 100 = 0.01 , for example 35% of 300 can be written as (35/100) × 300 = 105. (Our solved example in mathguru.com uses this concept)


Percentage increase and decrease

Sometimes 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:

1.  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.

2.  An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).

3.  A decrease of 60% means the final amount is 40% of the original (100% − 60% = 40%).

4.  A decrease of 100% means the final amount is zero (100% − 100% = 0%).(Our solved example in mathguru.com uses this concept)


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).

It is important to understand that percent changes, as they have been discussed here, do not add in the usual way, if applied sequentially. For example, if the 10% increase in price considered earlier (on the \($\)200 item, raising its price to \($\)220) is followed by a 10% decrease in the price (a decrease of \($\)22), the final price will be \($\)198, not the original price of \($\)200. The reason for the apparent discrepancy is that the two percent changes (+10% and −10%) are measured relative to different quantities (\($\)200 and \($\)220, respectively), and thus do not "cancel out".




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.