See Below.
Since the base is 3, the algorithm calls for repeatedly dividing by 3 until the number is reduced to zero.
100ten =
100 div 3 = 33 r 1; 33 div 3 = 11 r 0; 11 div 3 = 3 r 2; 3 div 3 = 1 r 0; 1 div 3 = 0 r 1
So 100ten = 102013.
Checking the answer:
102013 = 1 × 34 + 0 × 33 + 2 × 32 + 0 × 31 + 1 × 30
= 1 × 81 + 0 × 27 + 2 × 9 + 0 × 3 + 1
= 81 + 18 + 1 = 100
To convert from a representation in base three to a representation in base seven, use base ten as an intermediate: convert from base three into base ten, then from base ten to base seven.
What is the base 7 representation of 102013 ?