Quandaries and Queries
  

 

My son is in 5th grade.  He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.  Can you explain it to me in the simplest terms?
 
Thanks,
Karen
 

 

Hi Karen,

In our way of writing numbers in base 10 we write four-hundred and sixty two as 462, which really means

4100 + 610 + 2

or, to emphasize that is is base 10

4102 + 610 + 2.

Likewise

6453 = 6103 + 4102 + 510 + 2

The same convention with powers of the base is used in other bases. The number 241(base5) (which you should read two four one base five) is

252 + 45 + 1

But

252 + 45 + 1 = 225 + 45 + 1 = 71

Thus

241(base5) = 71(base10).

In a similar way

101101(base2)

is

125 + 024 + 123 + 122 + 02 + 1 = 32 + 8 + 4 + 1 = 45(base10)

I hope this helps,
Penny

 
 

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