1. ## Bases

Hi all.

I simply want to know what is the best way to do sums in different bases. Base 10 is easy and we can all do sums with it but what if I had 342 - 173. In base 10 the answer is 169. Fine. But how would I go about solving it in base 9 or 8? What difference, in my mind, do I need to apply to make it easier to do?

I have worked out that 169 in Base 9 is 207 and in Base 8 is 251 but I had to find the answer in Base 10 and then convert it and that just takes ages. There must be a simplier way.

Also, If anyway can find the thread about working out square roots without a calculator I would be grateful.

2. 342[8] - 173[8] = 147[8]

Do it like:
342
- 173
-------

Instead of "borrowing" 10, borrow 8. Instead of bumping a digit at 10, bump at 8.

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Newtons Approximation for Square Root

3. paultwant is, of course, completely correct- you add and subtract in other bases exactly like you do in base 10 except that you "carry" or "borrow" the base rather than 10.

A little more detail:
342- 173 (base 9)
Since "2" is smaller than "3" we "borrow 9: 9+ 2= 11 and 11- 3= 8 so we write "8" in the first place.
Since we "borrowed", we now have "3" rather than "4" in the second place (9 is 10 in base 9). 7 is larger than 3 we borrow again: 9+3= 12 and 12- 7= 5 so we write "5" in the second place.
Since we "borrowed", we now have "2" rather than "1" in the third place. 2- 1= 1 so we write "1" in the third place.
In base 9, 342- 173 is 158.