How do I convert 0.4166666666666 into a fraction?

Question

I know how to do a repeating decimal but not one that starts off regular and then becomes repeating.

Answer 1

just round it to .42

Answer 2

1/9 = 0.111...

2/9 = 0.222...

3/9 = 0.333...

4/9 = 0.444

.....

1/90 = 0.0111...

2/90 = 0.0222...

3/90 = 0.0333...

4/90 = 0.0444...

1/900 = 0.00111...

2/900 = 0.00222...

3/900 = 0.00333...

4/900 = 0.00444...

see the pattern?

0.41666... = 0.41 + 0.00666...

= 41/100 + 6/900

now just add them together and you'll get 5/12

hope it helps!

Answer 3

5/12 as a fraction.

As a decimal it would normally be "closed" at 0.41667, which is close enough for most purposes. Remember, if you keep repeating the "6" even to 100 decimal places, it is still not exact (because there should always be another one after it which you have omitted).