Review:
Fractions to decimals ...
7/25
3/8
7/10
5/12
Review:
Decimals to fractions ...
0.23
2.007
0.925
-0.48
TERMINATING AND
REPEATING DECIMALS
A decimal that ends or terminates.
EXAMPLE: 0.5 0.814 1.03
A decimal that ends with a
repeating digit or block of digits
_
__
EXAMPLE: 0.333
0.1212
Pull
REPEATING DECIMAL
Pull
TERMINATING
DECIMAL
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nts
Teacher's Notes
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Converting a Repeating Decimal to Fraction
Convert 0.8333…. to a fraction.
Steps:
o
nt
t
e.
2. Let n equal the decimal. Mark this as equation (1).
3. Take 10 to the power of the number of decimal digits up to the
repeating decimal digits. Here it is 1.
4. Multiply both sides of the equation by the power of 10. Simplify
and mark the equation as (2).
5. Now, subtract (1) from (2).
6. Solve the resultant equation to get the value of n in the simplest form.
Example
nt
Teacher's Notes
nt
1. Choose a repeating decimal number.
Converting a Repeating Decimal to Fraction
0.4
n = 0.4
10n = 4.4
-n - 0.4
9n = 4
4
n=9
0.63
n = 0.63
100n = 63.63
-n - 0.63
99n = 63
7
63
=
n = 99 11
0.583
n =0.583
100n = 58.33
-n - 0.583
99n = 57.75
n=
57.75 = 5775 = 7
99
9900 12
Converting a Repeating Decimal to Fraction
1/9 =
1/99 =
1/999 =
2/9 =
2/99 =
2/999 =
3/9 =
3/99 =
4/9 =
4/99 =
43/999 =
5/9 =
6/9 =
15/99 =
115/999 =
7/9 =
8/9 =
37/999 =
23/99 =
230/999 =
67/99 =
627/999 =