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# Relationships Between Percents, Fractions and Decimals Study Guide

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Updated on Oct 5, 2011

## Introduction to Relationships Between Percents, Fractions and Decimals

Mathematics is a language.

—JOSIAH WILLARD GIBBS, theoretical physicist (1839–1903)

This first percent lesson is an introduction to the concept of percents. It explains the relationships between percents, decimals, and fractions.

A percent is a special kind of fraction or part of something. The bottom number (the denominator) is always 100. For example, 5% is the same as Literally, the word percent means per 100 parts. The root cent means 100: A century is 100 years, there are 100 cents in a dollar, etc. Thus, 5% means 5 parts out of 100. Fractions can also be expressed as decimals: is equivalent to 0.05 (five-hundredths). Therefore, 5% is also equivalent to the decimal 0.05.

You come into contact with percents every day: Sales tax, interest, tips, inflation rates, and discounts are just a few common examples.

If you're shaky on fractions, you may want to review the fraction lessons before reading further.

#### Tip

Percentages are only used in writing and are never used in calculations. The percent symbol (%) looks like a jumbled up "100," so that should help remind you to always change your percentages to a fraction over 100 before doing any algebraic calculations! Example: 37.5% = or

## Changing Percents to Decimals

To change a percent to a decimal, drop the percent sign and move the decimal point two digits to the left. Remember: If a number doesn't have a decimal point, it's assumed to be at the right. If there aren't enough digits to move the decimal point, add zeros on the left before moving the decimal point.

Example: Change 20% to a decimal.

 1 Drop the percent sign: 20 2 There's no decimal point, so put it at the right: 20. 3 Move the decimal point two digits to the left:
 Thus, 20% is equivalent to 0.20, which is the same as 0.2.
 (Remember: Zeros at the right of a decimal don't change its value.)

## Changing Decimals to Percents

To change a decimal to a percent, move the decimal point two digits to the right. If there aren't enough digits to move the decimal point, add zeros on the right before moving the decimal point. If the decimal point moves to the very right of the number, don't write the decimal point. Finally, tack on a percent sign (%) at the end.

Example: Change 0.2 to a percent.

 1 Move the decimal point two digits to the right after adding one zero on the right so there are enough decimal digits: 2 The decimal point moved to the very right, so remove it: 20 3 Tack on a percent sign: 20%
 Thus, 0.2 is equivalent to 20%.

#### Tip

When changing decimals to percentages, remember that a mixed decimal is always going to be more than 100%. Example: 1 = 100% and 2.75 = 275%

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