Question

Use the infinite geometric sum formula to write 0.757575... as a fraction in reduced form. Show all steps.

I'm so confused on how to do this and would really appreciate some help!

Answer 1

Convert to a fraction by placing the decimal number over a power of 10.30303/40000

If this helped please give stars and a thanks ^.^ much appreciated!

Answer 2

75/99.

Explanation:

The infinite geometric sum formula when
`r<1` is

`\sum ar^(n)=(a)/(1-r)`

So, we know that

`a=(75)/(100)`, because it represents the beginning of the number.

`r=(1)/(100)`, because the periodic number repeats each two digits.

Replacing these values, we have

`\sum ((75)/(100) )((1)/(100))^(n)=((75)/(100) )/(1-(1)/(100))\\((75)/(100))/((100-1)/(100) )=((75)/(100) )/((99)/(100) )=(75)/(99)=0.75757575...`

Therefore, the fraction would be 75/99.

If you wanna demonstrate this is true, you just have to divide, then the quotient will be a rational infinite number like the given one 0.757575...