SOLUTION: Change the numbers to the indicated base. 133 to base four 5881 to base nine

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Change the numbers to the indicated base. 133 to base four 5881 to base nine      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 348548: Change the numbers to the indicated base.
133 to base four
5881 to base nine
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
133 to base four :

3(10)=3(4)

30(10)=3*10(10)=3*22(4)=3*2(4)+3*20(4)=12(4)+120(4)=132(4)

100(10)=10(10)+3*30(10)=22(4)+3*132(4)=22(4)+3*2(4)+3*30(4)+3*100(4)
=22(4)+12(4)+210(4)+300(4)
=32(4)+2(4)+1110(4)=100(4)+1110(4)=1210(4)

hence 133(10)=3(4)+132(4)+1210(4)=201(4)+1210(4)=2011(4)

Verif : 1+4+2*64=5+2*64=128+5=133
---------

5881 to base nine (default : from base 10)
81(10)=9*9=100(9)

800(10)=8*100(10)=8*10(10)*10(10)=8*11(9)*11(9)=8=8=8*121(9)=1078(9)

5000(10)=5*121(9)*10(10)=5*121(9)*11(9)=5=5*1331(9)
=6765(9)

100(9)+1078(9)+6765(9)=1178(9)+6765(9)=8054(9)

Verif : 4+5*9+8*9^3=49+8*729=49+5832=5881