Question

Convert 5.764764764 … to a rational expression in the form of a over b, where b ≠ 0.

Answer 1

what are the answer choises? do you know where to start?

Answer 2

choices:

5 and 764 over 999
5764 over 9999
5 and 764 over 99
5 and 999 over 764

Answer 3

set the whole number 5 aside, and look at the decimal part only

0.764764764...

now, let's set up an equation where x = the repeating part of the decimal

x = 0.764764764... let's call this equation (1)

since there are three repeating digits, let's multiply both sides by 10^3 (you'll see why in a bit)

10^3 * x = 764.764764... let's call this equation (2)

subtract equation (2) - equation (1). when you subtract the 764.764764... - 0.764764.... etc. the decimal parts cancel out and you should end up with a whole number on the other side. solving this new equation for x will give you x as a fraction. recall that x stands for the repeated decimal part; you have successfully converted the repeating decimal to a fraction.

from there, add back the whole number 5 to the beginning. however, since it wants it in the form a/b rather than a mixed number, convert your mixed number to an improper fraction.