Question

0.1(9) repeating as a decimal.

Answer 1

0.2

Explanation:

You want to know the value of 0.199...repeating 9s.

Value

Let the value be represented by x:

x = 0.1999...

Then 10x is ...

10x = 1.9999...

The difference is ...

10x -x = 1.9999... -0.1999... = 1.8

9x = 1.8 . . . . . simplify

x = 1.8/9 = 0.2

The value of the repeating decimal is 0.2.

__

Additional comment

The repeating decimal 0.99... is equivalent to 9/9 = 1. The repeating portion of 0.1999... has the value 0.1, Added to the first non-repeating digit, the sum is ...

`0.1\overline{9}=0.1+0.0\overline{9}=0.1+0.1=0.2`