Division with decimal in the divisor I understand HOW to do division with a decimal in the divisor, but my question is MUST we remove the decimal in the divisor and if so, why?
Thanks.
 A: Remember that the word decimal is a shortened form of decimal fraction, meaning a fraction whose denominator is a power of $10$.  For example,
$$
3.14 = \frac{314}{100},
\qquad
0.0625 = \frac{625}{1000},
\qquad
5280.1 = \frac{52801}{10}.
$$

As an example, consider the division problem
$$
\frac{9.6}{3.84} = \frac{\frac{96}{10}}{\frac{384}{100}}
= \frac{96}{10} \cdot \frac{100}{384}
= \frac{96}{384} \cdot \frac{100}{10}
= \frac{96}{384} \cdot 10.
$$
This last form shows you that the original division calculation is equivalent the quotient of the whole numbers$96$ and $384$, as long as you adjust by a factor of $10$ afterwards.  (This is usually described as moving the decimal point.)
In order to actually do this calculation, you can multiply the numerator by a sufficiently large power of $10$ to make it a multiple of the denominator, making sure to divide by that same power of $10$ afterwards to compensate.  Note:  it won't always be the case that you get precisely a multiple, no matter how large a power of $10$ you multiply by.  In this case,
$$
\frac{96}{384} \cdot 10 = \frac{96}{384} \cdot \frac{100}{100} \cdot 10
= \frac{9600}{384} \cdot \frac{10}{100}
= 25 \cdot \frac{1}{10}
= \frac{25}{10}
= 2.5.
$$
The upshot:  the integer fact that $384 \cdot 25 = 9600$ is responsible for all of the following:
$$
\cdots
= \frac{0.0096}{0.00384}
= \frac{0.096}{0.0384}
= \frac{0.96}{0.384}
= \frac{9.6}{3.84}
= \frac{96}{38.4}
= \frac{960}{384}
= \frac{9600}{3840}
= \cdots
= 2.5
$$
