Posted by Renee on Sunday, May 15, 2011 at 1:40pm.
Do you mean to convert 43_{5} to base 10?
In base 10, we have the right most digit to represent 0 to 9, the second (from right) to represent 10 (=10²), the rhidr to represent 100 (=10³)and so on.
The same goes with base 5, the right-most digit stands for 0 to 4 (1 less than 5), and the second digit for 5, the third for 5²=25, etc.
So 43_{5} = 4*5+3 = 23_{10}.
Notice that students in North America should be able to do interconversion between bases 5 and 10 without difficulties, thanks to the money system.
Consider base 5 as:
1 (1 cent)
5 (1 5-cents, or nickel)
25 (1 25-cents, or quarter).
43_{5} would be equivalent to 4 nickels and 3 cents, which make 23 cents.
Conversely, to convert from base 10 to base 5, we simply express the amount (up to $1.04) in cents, nickels and quarters. For example,
79_{10}
=79 cents
=3 quarters and 4 cents
=304_{5}
represent 555 in base 5