1. ## Recurring decimals

Hello everyone!

Question
Change 3/11 into a recurring decimal. (no calculator).

I started by thinking what 1/10 was and trying to work from there, but it didn't help. Help!

2. Hello,

Do you remember how to do a division at school ?

First, you divide 3 by 11. The quotient is 0, the remainder is 3. Then, put a coma and calculate 30/11. The quotient is 2, the remainder is 8.

etc...

And there will be a time when you will have 3 as a remainder. It'll be the same numbers as previously, and here is the period.

3. so, it's like a sequence

3/11 , 30/11 , 300/11
0 r3 2 r8 27 r3

giving 0.27...

thats about as far as I could do it without a calculator!

there is always a remainder, so it will always carry on, but i don't understand the bit about 'there will be a time when you will have 3 as a remainder'

thanks.

4. Ouap, that's not like this i meant to do ^^

D'you see the thing ?

5. Sorry, I don't understand what you have done there.

6. ## I think

the easiest way to do it if you are trying to do what I think you are is this...to get a repeating number you must have it over all nines...so to have a repeating number that repeats every two numbers you must have it over 99 so rewrite $\frac{3}{11}$ as $\frac{27}{99}$ and now you know that the repeated decimal equivalent is $.2727272727$

7. Originally Posted by Mathstud28
the easiest way to do it if you are trying to do what I think you are is this...to get a repeating number you must have it over all nines...so to have a repeating number that repeats every two numbers you must have it over 99 so rewrite $\frac{3}{11}$ as $\frac{27}{99}$ and now you know that the repeated decimal equivalent is $.2727272727$
Yes. I got it now! Thanks.