# 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.