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March 27, 2015

Posted by **Renee** on Sunday, May 15, 2011 at 1:40pm.

43

5

- math -
**MathMate**, Sunday, May 15, 2011 at 2:05pmDo 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}

- Claret Maths -
**Kevin**, Monday, June 3, 2013 at 10:48amrepresent 555 in base 5

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