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Sagot :
To convert a number in base 10 to a number in base five we need to divide the number by 5 and find its reminder for the firt step we would have:
[tex]\frac{3278}{5}=655.6[/tex]since we have a decimal part this means that it has a remainder, to find it we mutiply the integer part of the previus result to five and subtract the result from 3278, then we have:
[tex]3278-(5)(655)=3[/tex]This means that our first remainder is 3.
Now we need to divide the previous interger result (655) by 5 and then find the remainder as we did before:
[tex]\frac{655}{5}=131[/tex]Since this result does not have decimal part the remainder is zero.
This means that our second remainder is 0.
We apply the same procedure till we have a quotient in which the result is less than 5, then we will have:
[tex]\begin{gathered} \frac{131}{5}=26.2\text{ Integer result 26, remainder 1} \\ \frac{26}{5}=5\text{ Integer result 5, remainder 1} \\ \frac{5}{5}=1\text{ Interger result 1, remainder 0} \\ \frac{1}{5}=0\text{ Integer result 0, remainder 1} \end{gathered}[/tex]This means that our remainders are 3, 0, 1, 1, 0, 1.
The number in base 5 is the number formed bu the remainders in the opposite order, therefore:
[tex]3272=(101103)_5[/tex]
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