Question

Please answer attached photo!

Answer 1

Explanation:

The idea is to move the decimal to right after the repeating digit and then to right before it and subtract.

Let x = .46666

Then to move the decimal one place to right before the repeating digit, we multiply by ten which moves the decimal right after the 4 and right before the repeating 6:

10x = 4.666

Now we need to move it to right after the repeating digit, so we multiply by 100:

100x = 46.666 and subtract:

100x = 46.666

-10x = 4.666

99x = 42 so

x = 42/99