Question

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

Answer 1

Answer:

75/99.

Step-by-step explanation:

The infinite geometric sum formula when $r$ is

$\sum ar^{n}=\frac{a}{1-r}$

So, we know that

$a=\frac{75}{100}$, because it represents the beginning of the number.

$r=\frac{1}{100}$, because the periodic number repeats each two digits.

Replacing these values, we have

$\sum (\frac{75}{100} )(\frac{1}{100})^{n}=\frac{\frac{75}{100} }{1-\frac{1}{100}}\\\frac{\frac{75}{100}}{\frac{100-1}{100} }=\frac{\frac{75}{100} }{\frac{99}{100} }=\frac{75}{99}=0.75757575...$

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...

Answer 2

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

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