Question

Write −1.111… as a mixed number in simplest form.

Answer 1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are
3
3
numbers to the right of the decimal point, place the decimal number over
10
3
10
3

(
1000
)
(
1000
)
. Next, add the whole number to the left of the decimal.
1
111
1000

Answer 2

-1 ¹/₉

Explanation:

Firstly, let:

x = -1.111...

This means:
10x = -11.111...

Then:

10x - x = -11.111... - (-1.111...)

9x = -11.111... + 1.111...

9x = -10

x = -¹⁰/₉

x = -(⁹/₉ + ¹/₉)

x = -1 ¹/₉