# explorations in math

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convert the numeral to a numeral in base 10
14
5

• explorations in math -

The "1" stands for 5 in base 5.

145
=(1*5)+4
=?

• explorations in math -

4.5 + 1.1
20 + 1

21

• explorations in math -

415
=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:

3217
=3*7^2 + 2*7^1 + 1*7^0
=3*49 + 2*7 + 1*1
=147 + 14 + 1
=162

So
415
=4*5^1 + 1*5^0
=4*5 + 1*1
=21

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