### Converting Fractions, Decimals, and Percents Worksheets

Percents are widely used in business and everyday life. Business professionals use percent to calculate percent of loss or profit, and percent of increase or decrease in transactions such as sales, cost and expenses. Retailers and dealers use percent to give discount to their customers. Consumers are concerned with the percent of change of prices while employees are worried with the percent of their salaries paid in taxes.

The usual way of computing parts of the whole given the rate in terms of percent is to convert the rate in percent form to decimal. Other professionals convert the rate in percent to fraction and compute the percentage. Take note that percentage is different from the percent. Percentage is a number part of a whole while percent is the rate of the part of the whole. Rate is usually written in percent form, i.e. with percent sign (%).

Converting Decimal to Fraction

To convert a terminating decimal to a fraction, we take the whole number plus the decimal part of the given decimal number as the numerator of a common fraction with a denominator of the power of 10 of the given decimal.

Example:

$1.\;\; 0.15=\frac{15}{10^2}=\frac{15}{100}$
$2.\;\; 1.075=1\frac{75}{10^3}=\frac{75}{1000}$
$3.\;\; 0.0035=\frac{35}{10^4}=\frac{35}{10000}$

To convert a repeating decimal to a fraction, represent each repeating digit by 9 and each non-repeating digit by 0 in the denominator. The numerator is the difference between the number formed by the decimal digits and number formed by the digits that do no repeat.

Example:

$1.\;\; 0.1\bar{5}=\frac{15-1}{90}=\frac{14}{90}=\frac{7}{45}$
$2.\;\; 1.2\overline{4565}=1+\frac{124565-12}{99990}=\frac{124553}{99990}$

Converting Decimal to Percent

To change a decimal to a percent, move the decimal point two places to the right and annex the percent sign (%).

Example:

$1.\;\; 0.15=15\%$
$2.\;\; 1.13=113\%$
$3.\;\; 0.0000124=0.00124\%$

Converting Percent to Decimal

To change a percent to a decimal, move the decimal point two places to the left and remove the percent sign (%).

Example:

$1.\;\; 89.59\%=0.8959$
$2.\;\; 1234\%=12.34$
$3.\;\; 0.00578\%=0.0000578$

Converting Percent to Fraction

To change a percent to a fraction, transform percent to decimal first then change the decimal to fraction. Reduce the resulting fraction as needed. If percent involves a repeating decimal, just express percent in fraction form.

Example:

$1.\;\; 10\%=0.10=\frac{10}{100}=\frac{1}{10}$
$2.\;\; 5\frac{1}{2}=5.5\%=0.055=\frac{55}{1000}=\frac{11}{200}$
$3.\;\; 3\frac{1}{3}\%=\frac{10}{3}\%=\frac{10}{3}\times\frac{1}{100}=\frac{1}{30}$

Converting Fraction to Decimal

To transform fraction to decimal, just divide the numerator by the denominator.

Example:

$1.\;\; \frac{1}{4}=0.25$
$2.\;\; \frac{1}{3}=0.\overline{3}$

Converting Fraction to Percent

To change fraction to percent, change the fraction to decimal then change the decimal to percent.

Example:

$1.\;\; \frac{1}{5}=0.2=20\%$
$2.\;\; 1\frac{1}{2}=1.5=150\%$

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