## 6.8 Outline

- Percent
- Fractions/decimals/percents
- procedure for changing a percent to a decimal
- fraction/decimal/percent conversion chart

- Estimation
- unit fraction-conversion method
- percentage
- unit fraction comparison

- The percent problem
- the amount; percentage
- percent; rate
- whole quantity; base
- procedure
- warning: DO NOT ADD PERCENTS

## 6.8 Essential Ideas

**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 multiply 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 percent 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 whole quantity; it is preceded by the word *of*.

*Finally,* the remaining quantity is the partial amount; it is the numerator of the second fraction in the proportion: *P/100 = A/W*.