Percent Decrease

Percent Decrease Calculation:

•  i =

  Initial Value

  Starting value that will decrease

•  p =

  Decrease Percent

  Percent of initial value to decrease initial value by

•  f =

  Final Value

  Initial value minus percent decrease, in same units as the initial value

• -3 -2 -1 0 1 2 3 4 5 6 7 8 9

  Decimals

  Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Percent Decrease Formula

Percent decrease combines the original value with a percentage of that value in a subtractive way. If the percent change is negative this will be the same as a percent increase.

A percent is the ratio of any value out of 100. In the formula above we divide "p", the decrease percent, by 100 and multiply that by the initial value, "i", to find the percent of the initial value. The decrease percent of the original value, calculated by | i | * (p / 100), is then subtracted from the initial value to complete the calculation of percent decrease.

The vertical bars "|" in the formula mean to take the unsigned, non-negative, value. This step is required for initial values that are negative so they will decrease or increase in the correct direction, i.e. a 10% decrease to -50 should result in a final value of -55.

Percent Decrease Variables

A number can be decreased by a specified percent. We know percent will always be some value over 100 and is a unitless measure. Therefore, the final value will retain the units of the initial value.

Initial Value (i)

A starting number to decrease by some percent of itself. It may be a decimal or negative number. The final value will take on the dimensions of this number. If the number is a speed measurement in miles per hour the final value will also be miles per hour, if the initial value is a price in dollars the final value will be the new price in dollars.

Percent Decrease (p)

Percent to decrease the initial value by. This value may be given with a decimal or as a negative. If the value is negative the result will be an increase from the initial value.

Final Value (f)

Newly calculated value after changing by the given percent of the initial value. This value will have the same units (dimensions) as the initial value.

Percent Decrease Solution

What is a 5 percent decrease from 30?

Decreasing 30 by 5% results in a final value of 28.5.

Percent Decrease Example 160 pounds decrease by 4 percent

What will a person's final weight be if their initial weight of 160 pounds decreases by 4 percent?

A four percent decrease in weight from an initial weight of 160 pounds (lbs) results in a final weight of 153.6 lbs. The final value takes on the same unit dimensions as the initial value, pounds in this case.

Percent Decrease Example 200 decreases by -15 percent.

Initial value of 200 is set to decrease by -15 percent. The percent decrease is a negative number and because a negative and a negative make a positive the result will be an increase of the initial value.

A decrease of a value by some negative value is an increase. Changing an initial value of 200 by -15 percent results in a final value of 230.