BAse

[Guest]

I am having a little trouble:
How can I convert each of the following base ten numeral into its numeral in the base reguested?
142 in base twelve
72 in base two
231 in base eight
How can I find the missing base
28= 34 ___

 

[Gene]

The procedure is the same for all. My favorite is write the number, divide by the base, write the remainder to the right. Do it over till you get a zero then read down.

          0  11
         11  10 
12 into 142

= 11 10
probably written BA₁₂
Checking 12^1*11+12^0*10 =142

         0  1
         1  0
         2  0
         4  1
         9  0
        18  0
        36  0
2 into  72

= 1 001 000₂
Checking 2^6*1+2^3*1=72

         0  3
         3  4
        28  7
8 into 231

= 347₈
Checking 8^2*3+8^1*4+8^0*7=231

If you don't like that method you can find the highest power of the base smaller than the number, divide that into the number and write the dividend, subtract dividend*base^power from the number and repeat. The base 8 would be

8^2=64
231/64=3       3
231-64*3=39
8^1=8
39/8=4         4
39-8*4=7
8^0=1
7/1=7          7

= 347₈

The last one
2*base+8=34
2*base=26
base=13