Question Number 209167 by lmcp1203 last updated on 02/Jul/24
$${please}\:{convert}\:\:\mathrm{2531}_{\left(\mathrm{5000}\right)\:} {to}\:\:{base}\:\mathrm{5002}.\:\:{thanks}.\:\: \\ $$
Answered by mr W last updated on 03/Jul/24
![2531_((5000)) =2×5000^3 +5×5000^2 +3×5000+1 =250 125 015 001 =1×5002^3 +4995×5002^2 +6×5002+5001 ⇒2531_((5000)) =[1d_(4995) 6d_(5001) ]_((5002))](https://www.tinkutara.com/question/Q209184.png)
$$\mathrm{2531}_{\left(\mathrm{5000}\right)} =\mathrm{2}×\mathrm{5000}^{\mathrm{3}} +\mathrm{5}×\mathrm{5000}^{\mathrm{2}} +\mathrm{3}×\mathrm{5000}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{250}\:\mathrm{125}\:\mathrm{015}\:\mathrm{001} \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{1}×\mathrm{5002}^{\mathrm{3}} +\mathrm{4995}×\mathrm{5002}^{\mathrm{2}} +\mathrm{6}×\mathrm{5002}+\mathrm{5001} \\ $$$$\Rightarrow\mathrm{2531}_{\left(\mathrm{5000}\right)} =\left[\mathrm{1}{d}_{\mathrm{4995}} \mathrm{6}{d}_{\mathrm{5001}} \right]_{\left(\mathrm{5002}\right)} \\ $$
Answered by lmcp1203 last updated on 03/Jul/24
$${thanks}. \\ $$