Directions:
Ten is not the only base we can write numbers in.
For example, we can write the number $100$ in base $8$.
To do this we need to fill in the blanks below in a way that makes the statement below true.
Also, each number must be a number between 0 and 7.
$$100=\underline{\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }}\cdot 64 + \underline{\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }} \cdot 8 + \underline{\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }} \cdot 1$$
To do this divide $64$ into $100.$ It goes in once. So the the first number is $1.$
What's left over? Answer: $100-64=36.$
We now divide $8$ into $36.$ It goes in $4$ times. So the second number is $4.$
What's left over? Answer: $36-4 \cdot 8=4$.
We now divide $1$ into $4.$ It goes in $4$ times. So the last number is $4.$
So,
$$100=1 \cdot 64 + 4 \cdot 8 + 4 \cdot 1.$$
We may write this as $100=(1,4,4)_8$.
Your problem of the week is to write the number $230$ in base $8.$