4. Finding Sums of Infinite Geometric Series
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We want to write the repeating decimal 0.555… as a fraction. To do so, we will start by writing this number as a sum of decimals and as a sum of fractions.
Number | 0.555… |
---|---|
Sum of Decimals | 0.5+0.05+0.005+… |
Sum of Fractions | 105+1005+10005+… |
a1=105, a2=1005
ba÷dc=ba⋅cd
Split into factors
Cancel out common factors
Simplify quotient and product
r=101, a1=105
Rewrite 1 as 1010
Subtract fractions
ba=a÷b
ba÷dc=ba⋅cd
Multiply fractions
ba=b/10a/10