explorations in math
posted by katie .
convert the numeral to a numeral in base 10
14
5

The "1" stands for 5 in base 5.
14_{5}
=(1*5)+4
=? 
4.5 + 1.1
20 + 1
21 
Your working is for
41_{5}
=4.5 + 1.1
=20 + 1
=21
The units digit is multiplied by 1, and the second digit from the right is multiplied by the base, 5 in this case.
If the number has more than 2 digits, the next digits (to the left) are multiplied by the subsequent powers of the base.
Example:
321_{7}
=3*7^2 + 2*7^1 + 1*7^0
=3*49 + 2*7 + 1*1
=147 + 14 + 1
=162
So
41_{5}
=4*5^1 + 1*5^0
=4*5 + 1*1
=21