while dividing $1\over11$ we get Quotient$ = 0.090909$ and Remainder$ = 1$ but when we apply Dividend$ = $Divisor$\times$Quotient$ + $Remainder, this equation is not satisfied.
What is the reason behind this?
[Math] dividend = divisor*quotient + remainder for rational number
divisibilitylinear algebra
Best Answer
"while dividing 1/11 we get quotient = 0.090909 and reminder = 1"
No. You do not.
If you divide $11$ into $1$ we find $11 < 1$ so so $11$ goes into $1$, $0$ times so the quotient is $0$ and we have remainder $1$.
And we apply that to $dividend = divisor*quotient + remainder$ we get:
$1 = 11*0 + 1$
which is ... perfect.
You probably went past the decimal point while dividing.
The thing is if you go past the decimal point you are multiplying the dividend by a power of $10$ for every decimal place. That means you will have to divide the remainder by the same powers of $1$.
So if you divided and got $quotient = 0.09090909$ and stopped you went past the decimal place $8$ places.
What that really means is you divided $10^8$ by eleven and got a quotient of $9090909$ and a remainder of $1$. This works. $10^8 = 11*9090909 + 1 = 99999999 + 1 = 100000000 = 10^8$.
But we divide everything by $10^8$ to have a $quotient = 0.09090909$ and a $remainder = 0.00000001$. ANd our equation is $1 = 11*0.09090909 + 0.00000001 = 0.99999999 + 0.00000001 = 1.00000000$.
And that's just fine.
Everything is fine.