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 (fivehundredths). 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%

Changing Percents to Fractions
To change a percent to a fraction, remove the percent sign and write the number over 100; then reduce if possible.
Example: Change 20% to a fraction.
1. 
Remove the % and write the fraction 20 over 100: 

2. 
Reduce: 

Example: Change 16 to a fraction.
1. 
Remove the % and write the fraction 16% over 100: 

2. 
Since a fraction means "top number divided by bottom number," rewrite the fraction as a division problem: 

3. 
Change the mixed number (16) to an improper fraction (): 

4. 
Flip the second fraction () and multiply: 

Changing Fractions to Percents
To change a fraction to a percent, there are two techniques. Each is illustrated by changing the fraction to a percent.
Common Equivalences of Percents, Fractions, and Decimals
You may find that it is sometimes more convenient to work with a percent as a fraction or as a decimal. Rather than having to calculate the equivalent fraction or decimal, consider memorizing the following equivalence table. Not only is this practical for reallife situations, but it will also increase your efficiency on a math test. For example, suppose you have to calculate 50% of some number. Looking at the table, you can see that 50% of a number is the same as half of that number, which is easier to figure out!
Practice
After memorizing the table, cover up any two columns with a piece of paper and write the equivalences. Check your work to see how many numbers you remembered correctly. Do this exercise several times, with sufficient time between to truly test your memory.
Tip
Find out what your local sales tax is. (Some places have a sales tax of 3% or 6.5%, for example.) Try your hand at converting that percentage into a fraction and reducing it to its lowest terms. Then, go back to the original sales tax percentage and convert it into a decimal. Now you'll be able to recognize your sales tax no matter what form it's written in. Try the same thing with other percentages you come across during the day, such as price discounts or the percentage of your paycheck that's deducted for federal or state tax.

Relationships Between Percents, Fractions and Decimals Sample Questions
 Change 75% to a decimal.
 Change 0.875 to a percent.
 Change 0.7 to a percent.
 Change 33to a fraction.
 Change to a percent.
Solutions to Sample Questions
Question 1
1. 
Drop off the percent sign: 
75 
2. 
There's no decimal point, so put one at the right: 
75. 
3. 
Move the decimal point two digits to the left: 

Thus, 75% is equivalent to 0.75. 

Question 2
1. 
Move the decimal point two digits to the right: 

2. 
Tack on a percent sign: 

Thus, 0.875 is equivalent to 87.5%. 
87.5% 
Question 3
Don't be tempted into thinking that 0.7 is 7%, because it's not!
1. 
Move the decimal point two digits to the right after 

tacking on a zero: 

2. 
Remove the decimal point because it's at the extreme right: 
70 
3. 
Tack on a percent sign: 

Thus, 0.7 is equivalent to 70%. 
70% 
Question 4
1. 
Remove the % and write the fraction over 100: 

2. 
Since a fraction means "top number divided by bottom number," 

rewrite the fraction as a division problem: 

3. 
Change the mixed number to an improper fraction : 
: 
4. 
Flip the second fraction and multiply: 

Thus, is equivalent to the fraction 
: 
Question 5
Technique 1:
1. 
Multiply by 100: 

2. 
Convert the improper fraction to a decimal: 


Thus, is equivalent to both . 
Technique 2:
1. 
Divide the fraction's bottom number (9) into the top number (1): 

2. 
Move the decimal point in the quotient two digits to the right 

and tack on a percent sign (%): 


Note: is equivalent to . 
Find practice problems and solutions for these concepts at Relationships Between Percents, Fractions and Decimals Practice Questions.
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From Practical Math Success in 20 Minutes A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.