What fraction is equal to 2.1637373737?

Answer 1

Take this apart in steps.

First, get the non-repeating part (2.16). This is (2 + 16/100)

The rest is 0.00·37· and can be written as (0.·37· / 100)

0.·37· is 37 / 99, so 0.00·37· would be (37 / 9900)

Putting it all together, you get:

2 + 16/100 + 37/9900

(19800 + 1584 + 37) / 9900

21421 / 9900 ■

Reading over this again, I make a note: When you have 1 repeating digit, it goes over 9. 2 repeating digits would go over 99, etc.

0.4444.... = 0.·4· = 4/9 0.25252525 = 0.·25· = 25/99