Section 6.8: Percent

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6.8 Outline

  1. Percent
  2. Fractions/decimals/percents
    1. procedure for changing a percent to a decimal
    2. fraction/decimal/percent conversion chart
  3. Estimation
    1. unit fraction-conversion method
    2. percentage
    3. unit fraction comparison
  4. The percent problem
    1. the amount; percentage
    2. percent; rate
    3. whole quantity; base
    4. procedure
    5. 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.