What is - 1.111 ... as mixed fraction

Step-by-step explanation:

When you are changing a repeating decimal to a fraction, there is a trick you have to know. 2 actually. Put the decimal right before the repeating starts and right after the repeating starts. This one is a bit tricky since the decimal is after a 1, and 1 is what is repeating. So let's leave that one as is and simply say that

x = - 1.11111

Now let's move the decimal right after the second one. To do that you have to multiply by 10. So we then can say that

10x = - 11.11111

For this problem, we will disregard the negative til the end because it just makes things confusing.

Subtract the smaller equation from the larger:

10x = 11.111111

- 1x = 1.111111

and get

9x = 10

Divide both sides by 9 to get 10/9 which is 1 1/9 as a mixed fraction. Let's check it first to see if we're correct, then we'll throw the negative sign back on.

10/9 on your calculator gives you 1.111111111 repeating, so now that we know we are correct, the mixed fraction is

-1 1/9