Percentage - Calculations

Calculations

The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find the percentage of 50 apples out of 1250 apples, first compute the ratio 50/1250 = .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 5000, 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%.

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. A term such as (100/100)% would also be incorrect, this would be read as (1) percent even if the intent was to say 100%.)

The easy way to calculate addition in percentage (discount 10% + 5%):

For example, if a department store has a "10% + 5% discount," the total discount is not 15% but

y = (10\% + 5\%) - (10\% \times 5\%) = 15\% - 0.5\% = 14.5\%

Whenever we talk about a percentage, it is important to specify what it is relative to, i.e. what is the total that corresponds to 100%. The following problem illustrates this point.

In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female?

We are asked to compute the ratio of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that (60/100) × (5/100) = 3/100 or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at the answer: 3%/10% = 30/100 or 30% of all computer science majors are female.

This example is closely related to the concept of conditional probability.

Read more about this topic:  Percentage

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