<h3>
Answer: 13/99</h3>
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Work Shown:
The horizontal bar over the "13" means the 13 repeats forever like so
0.13131313...
Let's make x the value of this, so,
x = 0.131313...
Multiply both sides by 100
100x = 13.131313...
this moves the decimal point over 2 spots to the right. The decimal portion of 13.131313... is still the repeated "13" sequence
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We have
100x = 13.131313...
x = 0.131313...
Subtract straight down
100x-x becomes 99x
13.131313... - 0.131313... becomes 13. The decimal portions line up perfectly and subtract away.
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After those subtractions, we have 99x = 13 which solves to x = 13/99 when you divide both sides by 99
Use a calculator to confirm that 13/99 = 0.13131313...
Side note: since you're given a list of choices, you can use your calculator to try out each one and see which work and which don't work.
