How do you covert 3.6666.recurring into a fraction?

Answer 1

This is just a sick topic in general.

There's a lot of ways to go about it, but for this little guy in particular, its easy. It gets harder with numerous digits repeating.

First, cut the 3 out and focus on the repeated 6s after the decimal.

What fraction yields .6 repeating? 2/3 - Duh

So to convert the Mixed Number 3 2/3 into an Improper Fraction multiply denominator by the discarded 3 in the one's place before the decimal [3*3] and then add the numerator [(3*3)+2=11]. Put the calculated number over the denominator and call it a day.

11/3

Hope this helps.

Answer 2

Oh, dude, you want me to do math? Fine, I'll humor you. So, like, 3.6666... is the same as 3.6 with the 6 repeating, right? That's like 36/10 because the 6 keeps going forever, so it's 36 over 10. Simplify that and you get 18/5. Boom, fractionized. Math wizard strikes again.

Answer 3

To convert 3.6666... recurring into a fraction, we can represent it as x = 3.6666... and then subtract the non-recurring part from the recurring part. This gives us 100x = 366.6666... Subtracting x from 100x gives 99x = 363, so x = 363/99. Simplifying this fraction gives us x = 121/33, which is the fraction form of 3.6666... recurring.