General Contents
Detailed Contents
Index
Programmed tutorial: Repeating Decimal: Example 1
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Write the repeating decimal
as a geometric series and find its sum as the ratio of two integers.
General Contents
Detailed Contents
Index
What properties of a geometric series do we need to identify here?
We need the first term,
a
, and the ratio,
r
.
Can we factor?
Yes.
Rewrite with a factor and a sum of terms.
Does
this reveal
the ratio,
r
?
Yes.
Determine the ratio.
r = 0.01
What is the value of the first term,
a
?
a = 0.87.
Write the general equation for the sum of a geometric series?
Substitute values.
We use
Simplify.
Have we answered the question about the sum?
No.
What do we need to do further?
We need to find the result as the ratio of two integers.
How can we do that?
We can multiply both the numerator and the denominator by 100.
Do that.
We get
, a ratio of two integers.
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as a geometric series
and find its sum as the ratio of two integers.