233 base five = 2 x 5^2 + 3 x 5 + 3 x 1 = 2 x 25 + 15 + 3 = 50 + 18 = 68 base 10
11000 base two = 1 x 2^4 + 1 x 2^3 = 16 + 8 = 24 base ten
43E base twelve = 4 x 12^2 + 3 x 12 + 11 x 1 = 4 x 144 + 36 + 11 = 576 + 47 = 623 base ten
9.1/3575
use long division like this
_<u>0.</u>_________
3575|91.000000
we find how many of 3575 fit into the 91
it's too big so we go farther
how many 3575 go into 910
too big so we go farther
how many 3575 go into 9100
the answer is 2 so put that in the correct place and mulitply that and put that in the correct place. then we subtract
_<u>0.</u><u>02</u>_________
3575|91.000000
-<u>71.50</u>
19.50
bring down the next number
find how many go into 19.500
the answe ris 5
_<u>0.</u><u>02</u><u>5</u>_________
3575|91.000000
-<u>71.50</u>
19.500
-<u>17.875</u>
1.625
bring down he next zero ( I fast forward and skip steps for convinience)
__
_<u>0.</u><u>02</u><u>5</u><u>455</u>_________
3575|91.000000
-<u>71.50</u>
19.500
-<u>17.875</u>
1.6250
-<u>1.4300</u>
.19500
-<u>.17875
</u> 16250
-14300
and so on untill infinity so the answe ris 0.0254555555555555 (enless fives)
If you have a calculator, you can use the inverse cos " cos⁻¹ " key. Many upper level books write that as Arccos so as not to confuse you with a negative exponent. We do that because if you take the cosine of any angle, and then the inverse cosine of any angle, it leads you back to the original angle. Think of it as a big "UNDO" button.
To one decimal place, that result is 61.6 degrees.
