Question

Use divisions to convert the base ten numeral 107 to base five. How do I solve it?

Answer 1

To me, 10 = 5*2, hence \(10^0 = 5^0*2^0; 10^1=5^1*2^1;10^2=5^2*2^2\)
107 base 10 is \(7*(10^0) + 0*(10^1)+1*(10^2)\)
If we write it under the base 5, then, the number is under the form:
\(a*5^0+b*5^1+c*5^2+d*5^3+.....\)
now combine them
\(a*5^0 + b*5^1 +c*5^2 +d*5^3 +...= (7*2^0)*5^0+(0*2^1)*5^1 + (1*2^2)*5^2\)
Now, make comparison
we have a = 7 but in base 5, \( 7 = 2*5^0 +1*5^1\)
b = 0
c = 4
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it becomes 412

Answer 2

if you want to use divisions (which is the fastest way) then

107/5=21 R 2
21/5=4 R 1
4/5 = 0 R4
so the answer is 412

Answer 3

wow!!