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Question Number 147611 by mathdanisur last updated on 22/Jul/21

(111)_(10)  = (x)_5   ⇒ x = ?

$$\left(\mathrm{111}\right)_{\mathrm{10}} \:=\:\left({x}\right)_{\mathrm{5}} \\ $$$$\Rightarrow\:{x}\:=\:? \\ $$

Answered by bobhans last updated on 22/Jul/21

(111)_(10) = 1×10^2 +1×10^1 +1×10^0 =111  ⇒111 =(421)_5  =4×5^2 +2×5^1 +1×5^0                 =100+10+1=111_5

$$\left(\mathrm{111}\right)_{\mathrm{10}} =\:\mathrm{1}×\mathrm{10}^{\mathrm{2}} +\mathrm{1}×\mathrm{10}^{\mathrm{1}} +\mathrm{1}×\mathrm{10}^{\mathrm{0}} =\mathrm{111} \\ $$$$\Rightarrow\mathrm{111}\:=\left(\mathrm{421}\right)_{\mathrm{5}} \:=\mathrm{4}×\mathrm{5}^{\mathrm{2}} +\mathrm{2}×\mathrm{5}^{\mathrm{1}} +\mathrm{1}×\mathrm{5}^{\mathrm{0}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{100}+\mathrm{10}+\mathrm{1}=\mathrm{111}_{\mathrm{5}} \\ $$

Commented by mathdanisur last updated on 22/Jul/21

Thankyou Sir, answer  421.?

$${Thankyou}\:{Sir},\:{answer}\:\:\mathrm{421}.? \\ $$

Commented by bobhans last updated on 22/Jul/21

yes

$$\mathrm{yes} \\ $$

Commented by mathdanisur last updated on 22/Jul/21

thanks Sir

$${thanks}\:{Sir} \\ $$

Answered by gsk2684 last updated on 22/Jul/21

5∣111  5∣22→1      4→2  (111)_(10) =(421)_5

$$\mathrm{5}\mid\mathrm{111} \\ $$$$\mathrm{5}\mid\mathrm{22}\rightarrow\mathrm{1} \\ $$$$\:\:\:\:\mathrm{4}\rightarrow\mathrm{2} \\ $$$$\left(\mathrm{111}\right)_{\mathrm{10}} =\left(\mathrm{421}\right)_{\mathrm{5}} \\ $$

Commented by mathdanisur last updated on 22/Jul/21

thankyou Sir

$${thankyou}\:{Sir} \\ $$

Answered by Rasheed.Sindhi last updated on 22/Jul/21

111_(10) =100+10+1                 =4×25+2×5+1                 =4×5^2 +2×5^1 +1                =421_5

$$\mathrm{111}_{\mathrm{10}} =\mathrm{100}+\mathrm{10}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{4}×\mathrm{25}+\mathrm{2}×\mathrm{5}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{4}×\mathrm{5}^{\mathrm{2}} +\mathrm{2}×\mathrm{5}^{\mathrm{1}} +\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{421}_{\mathrm{5}} \\ $$

Commented by mathdanisur last updated on 22/Jul/21

Thank you Sir

$${Thank}\:{you}\:{Sir} \\ $$

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