Lesson 6-5 Rational Numbers and Decimals
All fractions can be converted to a decimal by dividing the
numerator by the denominator.
Can be written as 1 ÷ 8.
8) 1.00
.125
Add the decimal
point and annex
zeros.
8) 1.000
-8
20
16
40
40
0
So the fraction
can be written as the terminating decimal
since it ends, 0.125.
If we take the fraction and convert it to a decimal we get the
decimal 0.33333… . This is called a repeating decimal. We can
show that the three repeats by using bar notation.
0.333333 = 0.3
Remember that the bar is placed only over the digit or digits
that repeat. So for the decimal 0.1545454…, the bar is placed
over the first 54.
0.1545454 = 0.154
To convert a decimal to a fraction place the decimal over its place
value position.
0.85 =
Then simplify. The GCF is 5.
=
Repeating decimals can be written as a fraction. We need to
look at how many digits repeat. For example, in 0.77777… only
one digit repeats where as in 0.161616… two digits repeat. We
can use algebra to help us do this.
The variable n represents our
n = 0.77777
fraction.
Multiply both sides of the
10n = 7.7777
equation by 10 to get a whole
number.
- n = 0.77777
Subtract the repeating decimal
part.
9n = 7
9
9
Divide both sides by 9.
n=
One digit that repeats multiply by 10. Two digits that repeat
multiply by 100. Three digits multiply by 1000 and so on.