Percentages

The words percent and percentage are everywhere. You will most likely encounter percentages, both as part of your day-to-day tasks and as part of your work including buying things, selling things, and paying people.

A percentage is a way of saying how large or small a quantity is compared to another quantity.

For the simplest things in life, simple words like "half" work fine. The old saying asks, "Is the glass half full or half empty?" The optimist looks at how much is in the glass. The pessimist looks at how little is in it. It is the same proportion, no matter what.

You use a percentage in three ways:

  1. To compare a quantity to the whole.
  2. To compare one quantity to another.
  3. To compare a quantity to an increased or decreased amount of the same quantity.

One big advantage of a percentage is that it applies to any quantity.

Percentage as Fraction

A percentage is a fraction, but the denominator never changes. What makes it special is that the dominator is always 100. For example, 17 percent is 17/100, a fraction with 100 in the denominator.

One half is 1/2, but when you convert that to a fraction with a denominator of 100, it becomes 50/100 or 50 percent.

The rule is to drop the percent sign and put the number in a fraction over 100. For example, to convert 26 percent to a fraction, 26/100 = 13/50.

Transforming fractions to percentages is the reverse of the conversion of percentages to fractions. The rule for converting a fraction to a percentage is to convert the fraction into a decimal and multiply by 100. The result is a percentage. For example, 33/100 is 0.33 and then multiply by 100 to arrive at 33 percent.

Percentage as Ratio

A percent is a fraction. A fraction is a ratio. Therefore, a percent is also a ratio. For example, 40:100 is 40 percent.

Percentage as Decimal

The rule for going from percentages to decimals is simple: Divide the percentage by 100. The result is a decimal number because the denominator in a percent is always 100. For example, 67 percent becomes 67/100 or 0.67. To divide by 100, you can just move the decimal point two places to the left of its original position.

Converting from a decimal number to a percentage is just the opposite of converting from a percentage to a decimal. To make this conversion, multiply the decimal by 100 and add a percent sign. The result is a percentage. For example, if you want to make 0.67 a percentage, multiply 0.67 by 100 to get 67 and then add a percent sign on it. As a shortcut, you can simply shift the decimal point two places to the right, which is the same as multiplying by 100.

Percentage Increases and Decreases

To increase a number by a percentage, multiply the original number by the percentage and then add the result to that original base amount. For example, if you normally supply customers with a Rs. 50.00 item and must increase its price by 15 percent, multiply Rs. 50.00 by 15 percent (50 × 0.15) to get Rs. 7.50. Add the result to the base amount to reach the new price: Rs. 50.00 + Rs. 7.50 = Rs. 57.50.

To decrease a number by a percentage, multiply that number by the percentage and then subtract the result from the base amount. For example, if you have a coupon for 20 percent off, and you want to buy a Rs. 50 item, multiply Rs. 50 by 20 percent (0.20) to get Rs. 10. That is the amount of your discount. Subtract the result from the base amount (Rs. 50 - Rs. 10 = Rs. 40) to get your final price.

To calculate a 100 percent increase in something, simply double the base amount. To calculate a 200 percent increase in something, simply triple the base amount.