what is 0.123124125... as a fraction?
To express the repeating decimal 0.123124125... as a fraction, we need to identify the repeating pattern. In this case, we can notice that the digits 123 repeat in the decimal.
Let's call the repeating part x, so we have x = 0.123124125...
Then, by multiplying both sides of the equation by 1000, we can move the decimal point three places to the right:
1000x = 123.124125...
Subtracting the original equation from the one with the decimal moved, we can eliminate the repeating part:
1000x - x = 123.124125... - 0.123124125...
Simplifying:
999x = 123
Dividing both sides by 999, we find:
x = 123/999
Therefore, the fraction representation of the repeating decimal 0.123124125... is 123/999.