Percent increase: finding the new amount

0:00A city has 603,500 people, and its population grows by 3.25 percent. How many people live there now?

0:10A percent increase means the amount grows by a percent of the starting amount. The start is 100 percent.

0:18First, write 3.25 percent as a decimal. Percent means out of 100, so divide by 100.

0:27That moves the decimal point two places left, so 3.25 percent is 0.0325.

0:36The increase is 3.25 percent of 603,500, so multiply 603,500 by 0.0325.

0:47That gives an increase of 19,613.75.

0:53Check in two parts: 3 percent of 603,500 is 18,105, and 0.25 percent is 1,508.75.

1:07Together they make 19,613.75, so the increase is right.

1:15Add the increase to the start: 603,500 plus 19,613.75 equals 623,113.75.

1:29People come in whole numbers, so round only at the very end: about 623,114 people.

1:38A faster way: the new amount is 100 percent plus 3.25 percent, which is 103.25 percent of the start.

1:48It is greater than 100 percent because the city has grown.

1:53As a decimal, 103.25 percent is 103.25 divided by 100, or 1.0325. This is the multiplier: the number we multiply by.

2:07603,500 times 1.0325 equals 623,113.75, the same answer in one step.

2:20A common mistake is adding 3.25 instead of 3.25 percent. That gives 603,503.25, which is far too small.

2:33So the city now has about 623,114 people.

2:40Recap: to increase by a percent, multiply by 100 percent plus that percent, written as a decimal.