Essential Ideas for Section 4.8

Percent

Percent is the ratio of a given number to 100. This means that a percent is the numerator of a fraction whose denominator is 100.

To change from fractional form to decimal form:

Divide the numerator (top) by the denominator (bottom). Write as a terminating or as a repeating decimal (bar notation).

To change from fractional form to percent form:

First change the fraction to a decimal, and then move the decimal point two places to the right and affix a percent symbol.

To change from a terminating decimal form to fractional form:

Write the decimal without the decimal point, and multliply by the decimal name of the last digit (rightmost digit).

To change from a terminating decimal form to percent form:

Shift the decimal point two places to the right and affix a percent symbol.

To change from percent form to fractional form:

Write as a ratio to 100 and reduce the fraction. If the percent involves a decimal, first write the decimal in fractional form, and then multiply by 1/100. If the percent involves a fraction, delete the percent symbol and multiply by 1/100.

To change from pecent form to decimal form:

Shift the decimal point two places to the left and delete the percent symbol. If the percent involves a fraction, first write the fraction as a decimal and then shift the decimal point.

The Percent Problem

A (this is the given amount) is P% (this is written as P/100) of W (this is the "whole quantity" and is follows the word "of").

Here is the procedure to follow:
First, identify the percent; write it as a fraction P/100.
Next, identify the wholde quantity; it is preceded by the word of.
Finally, the remaining quanity is the partial amount; it is the numerator of the second fraction in the proportion: P/100 = A/W.