mysteryrat
Answered

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 :

Slobs
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:

75/99.

Step-by-step explanation:

The infinite geometric sum formula when [tex]r<1[/tex] is

[tex]\sum ar^{n}=\frac{a}{1-r}[/tex]

So, we know that

[tex]a=\frac{75}{100}[/tex], because it represents the beginning of the number.

[tex]r=\frac{1}{100}[/tex], because the periodic number repeats each two digits.

Replacing these values, we have

[tex]\sum (\frac{75}{100} )(\frac{1}{100})^{n}=\frac{\frac{75}{100} }{1-\frac{1}{100}}\\\frac{\frac{75}{100}}{\frac{100-1}{100} }=\frac{\frac{75}{100} }{\frac{99}{100} }=\frac{75}{99}=0.75757575...[/tex]

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...

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