4. Which of the following formulas can be used to write 0.797979... as a fraction?

Answer:

The options are not shown, so i will answer this in a general way.

When we have a number like:

0.7979....

The steps to writing it as a fraction are the following ones:

1) First, you need to notice the repeating decimals.

In this case is easy to see that the repeating decimals are two, 7 - 9

2)we can multiply this number by 10^n, where n is the number of repeated decimals, in this case n = 2

10^2 = 100

then:

0.7979...*100 = 79.7979...

Now we can subtract the original number:

79.7979... - 0.7979 = 79

And this is equivalent to have:

0.7979..*100 - 0.7979... = 0.7979..*99 = 79

Then we know that if we multiply our number by 99, the outcome will be an integer.

Then we can multiply and divide by the same number (this is equivalent to multiply by one) as follows:

0.7979...*1 = 0.7979..*(99)/(99)  = (0.7979..*99)/99 = 79/99

Then:

0.7979... =  79/99

Answer:

[tex]S_{inf.} - \frac{\frac{79}{100} }{1-\frac{1}{100} }[/tex]

Pretend "inf." is the infinity symbol, I couldn't put the actual symbol. It's option B.

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