Question on some arithmetic calculations When $6272$ is multiplied by $0.94$ the answer is $5895.68$. When it is divided by $1.06$ the answer is $\approx 5916.9811$. Why is it so?
Just as a little background, I am using the default Microsoft calculator for this calculation. I haven't pulled out Mathematica yet. Could this be because of some weird variable conversion (int to double)? Any help would be much appreciated.
 A: If you take $5196$ and multiply it by $1.06 \times 0.94$ you are, in fact multiplying by a product of the form:
$$(1-x)(1+x)=1-x^2$$
In this case we have $x=0.06$. This is a useful thing to know if you are working with figures like this all the time (e.g. in finance, if prices go up 6% and then go down 6%, they end up a little lower).
A: You may be doing rounding too much and too early.  You may figure, correctly, that multiplying by $0.94$ is equivalent to dividing by $\frac{1}{0.94}$.
Calculate $\frac{1}{0.94}$. It is approximately $1.0638298$. You may have thrown away the part after the $1.06$, figuring it wouldn't make much difference. Well, percentagewise it is not much difference, but in dollars the difference is significant.
There is no mysterious fault in the Windows calculator, it is doing the calculation correctly, to good accuracy. To get good performance out of a calculator, let it do its thing, only round off at the end.
Remark: In general, if $a\ne 0$, multiplying by $a$ is equivalent to dividing by $\frac{1}{a}$.  
A: Because 
$$
6272(0.94) = 6272 \left(\dfrac{94}{100}\right)
$$
while
$$
\dfrac{6272}{1.06} =\dfrac{6272}{\dfrac{106}{100}} = 6272 \left(\dfrac{100}{106}\right).
$$
As you can see, 
$$
\dfrac{94}{100} \neq \dfrac{100}{106},
$$
because if the were then 
$$
106 \cdot 94 = 100 \cdot 100,
$$
which is not the case.
So the answers are different.
