what is the number 90.909090..... as a mixed number.
Hint: What does 10/11 equal?
That you so much it equals .90909090....
To express the recurring decimal 90.909090... as a mixed number, we need to follow a few steps.
First, let's observe that the repeating part of the decimal is 90.909090... To express it as a fraction, we can call the repeating part "x" and subtract it from the entire decimal:
90.909090... - x = 90
Now, we need to determine the value of "x" as a fraction. We can do this by noticing that the repeating part of the decimal is actually a repeating fraction. Specifically, we can express it as 0.9:
x = 0.9
To get rid of the decimal point, we can multiply both sides of the equation by 10 (to move the decimal one digit to the right):
10x = 9
Solving for x, we find:
x = 9/10
Now, let's substitute the value of "x" into our original equation:
90.909090... - 9/10 = 90
To simplify, we can convert 90 to an equivalent fraction with a denominator of 10:
90/1 = 900/10
Subtracting 9/10 from 900/10, we get:
900/10 - 9/10 = 891/10
Finally, we can express the mixed number form:
891/10 = 89 and 1/10
Therefore, the number 90.909090... as a mixed number is 89 and 1/10.