1. Decimals and Fractions
Applied Mathematics
Jefferson College ATS

2. Definitions
Decimal - Any number shown with a decimal point; a number based upon tenths or hundredths. ( 0.2, 0.375, 86.4 )
Fraction - One or more of the equal parts of a whole; a number usually expressed in the form a/b. ( 1/3, 2 5/8, 7/4 )

3. Converting Fractions to Decimals
To convert a fraction to a decimal, divide the numerator by the denominator. Do this until you get a decimal that terminates or repeats. If it repeats, place a bar (--- ) over the first number that repeats.
Example 1: Convert 3/4 to a decimal
3/4 = 3÷4= 0.75
( terminating decimal)
Example 2: Convert 2/3 to a decimal
2/3= 2÷3= ( repeating decimal )

4. Express fractions as percents by long division
You try:
Express fractions as percents by long division
87.5 %
0.875 =
125 %
1.25 =
37.5 %
.375 =

5. 1) 7/40
2) 7/50
3) 19/10
4)1/4
5)11/10
6)37/25
7)7/20
8)32/25
9)26/20

6. Converting Decimals to Fractions
In order to convert a decimal to a fraction, place the number that follows the decimal point over the place that it is in ( tenths, hundredths, thousandths, etc.). Then simplify as necessary.
Example 1: Convert 0.7 to a fraction
0.7= 7/10 ( 7 is in the tenths place )
Example 2: Convert 0.25 to a fraction
0.25= 25/100= 1/4 ( 25 is in the hundredths place. 1/4 is the simplified form of 25/100)
Example 3: Convert to a fraction
1.625= 1 625/1000= 1 5/8 ( 625 is in the thousandths place. 5/8 is the simplified form of 625/1000)

7. Convert decimal to base 10 fraction; simplify
You try
Convert decimal to base 10 fraction; simplify 8 4
0.8 = = 10 5 4 2 1
0.04 = = =
100 25 50 36 18 9
3.36 3 3 3 = = =
100 50 25

8. 1)0.866 =
2)0.428 =
3)0.3 =
4)0.41 =
5)0.992 =

9. 6) =
7) =
8)0.62 =
9) 1.22 =
10)0.19 =