write 0.366... as a fraction
To express 0.366... as a fraction, we can denote the repeating decimal as x:
x = 0.366...
We want to find a way to eliminate the decimal part of x. One way to do this is by multiplying x by a power of 10. Since there are three digits in the decimal part of x, we can multiply both sides of the equation by 10^3:
1000x = 366.366...
Next, subtract the original equation x from both sides:
1000x - x = 366.366... - 0.366...
999x = 366
To simplify the equation further, divide both sides by 999:
x = 366/999
Therefore, the fraction form of 0.366... is 366/999.