I am obtaining the exact same number as soon as doing so: $7 imes 10^2 + 2 imes10^1+7 imes10^0 = 727$, nothing changes.
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Help me number it out!
You should count in regards to $5^0, 5^1, 5^2, 5^3$ and also $5^4$, not in term of $100 ,10$ and $1$.
Start by the greatest power of $5$ smaller than your number, i.e. $5^4=625$ here, and also check how a lot you can multiply it without exceding (this will be a number in $1,2,3,4$).
Take the leftover (base 10, 727-625=102) and also repeat till you reach $0$.
You need to have$$eginalign727_10&= 625+100+2\&= 1 imes 5^4+4 imes 5^2+2 imes 5^0 \&= 10402_5.endalign$$
Trick: divide consecutively the quotients by $;5;$ and also save aside the residues :
Now put them in inverse order and voila!
Can you watch why it works?
You have to store dividing by $5$ and also create all the remainders.
$$727 = 5cdot 145 + 2$$$$145 = 5cdot29 + 0$$$$29 = 5cdot5 + 4$$$$5 = 5cdot1 + 0$$$$1 = 5cdot0 + 1$$
Write all the remainders in reverse: $10402$
And ta-da! Tbelow is your answer :-)
The trick is to realize thateginalign*727 &= 625 + 0*125 + 4*25 + 0*5 + 2 \ &= 5^4 + 0 *5^3 + 4*5^2 + 0*5^1 + 2*5^0.endalign*So the answer is $10402$.
You have to divide each number by 5 :
$$eginaligned727 &= 5 cdot 145 &+ colorred2\145 &= 5 cdot 29 &+ colorgreen0\29 &= 5 cdot 5 &+ colorblue4\5 &= 5 cdot 1 &+ colormagenta0\1 &= 5 cdot 0 &+ colorbrown1endaligned$$
Hence the answer is $colorbrown1colormagenta0colorblue4colorgreen0colorred2_5 = 1 cdot 5^4 + 0 cdot 5^3 + 4 cdot 5^2 + 0 cdot 5^1 + 2 cdot 5^0 = 727$
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