CBEST Math
Introduction
Decimals
Percents
Fractions
Relating Decimals, Fractions, and Percents
Sample Problems Worked Out
 

How Decimals, Fractions, and Percents are Related

     There is nothing really different between all three of these things. They are all different representation of the same thing. If you learn how to rewrite each one as one of the others, you are well on your way to increasing your passing probability.
     1) To change a decimal to a percent, move the decimal 2 places to the right, add the percent sign.
     2) To change a percent to a decimal, move the decimal 2 places to the right, drop the percent sign.
Examples:
.50 = 50%
.06 = 6%
4.5 = 450 %
.79 = 79%
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67% = .67
54.5% = .545
25% = .25
5% = .05
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Remember to add zeroes as place holders if you need them.
     3)To change a decimal to a fraction, look at the last number on the right. This tells you what your denominator is. The number on top are the important numbers in the decimal. We will only talk about decimals less than 1.
Example: Turn .45 into a fraction. The 5 is the last number. It is in the hundredths place. Therefore, we have 45 hundredths, or 45/100. Yes, it can be reduced.
Example: Turn .067 into a fraction. The last number is a 7. It is in the thousandths place. Therefore, we have sixty seven thousandths, or 67/100. The zero before the 6 was just a place holder.
Example: Turn .650 into a fraction. We have a zero on the end. It is in the thousandths place. Therefore, we have 650/1000. If there is a zero on the end, we can drop it and change .650 to .65. Then it is 65/100 which is an equivalent fraction to 650/1000.


     Learn your decimal places! The first place to the right of a decimal is tenths. All the rest are just a factor of ten more than the previous one-tenths, hundredths, thousandths, ten thousandths, etc. If you have trouble remembering, just think of how to write 10 cents as a decimal. It is written as .10 or .1. Ten cents is one tenth of a dollar. Therefore, .1 = 1 tenth, or even .10 which is 10/100 which reduces to 1/10.
     4) Changing a fraction to a decimal is the hardest. You divide the bottom number into the top.
Example: Change 3/8 into a decimal. 3/8 means 3 divided by 8. It goes .375.
     5) For changing a fraction to a percent, you need to first change it to a decimal, then a percent.
Example: Change 2/5 into a percent. 2 divided by 5 = .4, .4 as a percent equals 40%.
     The reason we did not do a whole lot with the preceding, is that you only need to familiarize yourself with #4 and #5 on an as needed basis. Use it as a last resort. However, you will should memorize the following:

Fractions, Decimals, and Percents That You Should Know

1/2 = .5 = 50%. Each half is worth 50% or .5 (or .50)
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1/3 = .33 = 33% (Thirds are all approximate values, but close enough)
2/3 = .66 = 66%. Each third is worth .33
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1/4 = .25 = 25%
2/4 = 1/2
3/4 = .75 = 75%. Each fourth is worth 25% or .25
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1/5 = .2 = 20%
2/5 = .4 = 40%
3/5 = .6 = 60%
4/5 = .8 = 80%. Each fifth is worth 20% or .2 (or .20)
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1/6 = .17 = 17% (Approximate value)
2/6 = 1/3 (See thirds. Sixths are equal to half of thirds)
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1/8 = .125 = 12.5%
2/8 = 1/4
3/8 = .375 = 37.5%
4/8 = 1/2
5/8 = .625 = 62.5%
6/8 = 3/4
7/8 = .875 = 87.5%. Each eighth is worth .125, which is half of a fourth.
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Ninths follow a pattern. All decimals are repeating, but we cut them off after 2. They repeat the number on top.
1/9 = .11 = 11% (Approximate values)
2/9 = .22 = 22%
3/9 = 1/3
4/9 = .44 = 44%
5/9 = .55 = 55%
6/9 = 2/3
7/9 = .77 = 77%
8/9 = .88 = 88%
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1/10 = .1 = 10%
2/10 = 1/5
3/10 = .3 = 30%
4/10 = 2/5
5/10 = 1/2
6/10 = 3/5
7/10 = 70%
8/10 = 4/5
9/10 = .9 = 90%. Each tenth is equal to .1.