If you can multiply a decimal, you can multiply a percent!

As discussed in our previous lectures on percentages, the key to any percentage problem is to change the number to a decimal first, and then perform the mathematical operation desired;

REMEMBER: A percentage is a just a different way to show a decimal number.

1. If the number is a decimal: moving the decimal place TWO spaces to the right and adding the % symbol, you can turn any decimal into a percentage.
2. If the number is a percentage: moving the decimal place TWO spaces to the left and deleting the % symbol, you can turn any percentage into a decimal.

For example (decimal to percentage):

.83 = 83% (moved decimal two spaces to the right and added the % symbol).

.21 = 21% (moved decimal two spaces to the right and added the % symbol).

2 = 200% (there are imaginary zeros behind numbers...so this would end up being 2.00. (moved decimal two spaces to the right and added the % symbol).

.053 = 5.3% (moved decimal two spaces to the right and added the % symbol)...note here there is still a decimal in the percentage, as expected.

.003 = 0.3% (note that if there is a decimal place in front of the number AFTER you have moved it two spaces to the right, then the percentage is also expressed as a decimal, but with a % symbol). (moved decimal two spaces to the right and added the % symbol).

For example (percentage to decimal):

10% = .10 (moved the decimal place TWO spaces to the left and deleted the % symbol)

200% = 2 (moved the decimal place TWO spaces to the left and deleted the % symbol)

4.1% = .041 (moved the decimal place TWO spaces to the left and deleted the % symbol)

Perform the multiplication using decimal values, and then convert back to a percentage.

For example, multiplying 50% and 50% we would convert to .50 and .50, multiply, then convert back to a percentage: (move decimal place two spaces to the right and add the % symbol).

Once we have the .25 above, we convert back to a percentage by moving to the right two decimal points... thus, 25% is our answer.