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!
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.
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.
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 $\displaystyle \frac{3}{11}$ as $\displaystyle \frac{27}{99}$ and now you know that the repeated decimal equivalent is $\displaystyle .2727272727$