Dividing Decimals.. But remainders?

Question

So, I understand how to do long division with decimals.

So let's consider this problem:

$10.5$ divided by $5.5$ (I chose this problem because it will OBVIOUSLY have a remainder)

So we will look at is as $105$ div'd by $55$

We will get $1$ with the remainder of $50$... Now time to convert this back to decimals

Okay so Answer was 0.01 but how should I convert the remainder to a decimal?

Sorry, I'm in 5th grade, and this is my first time posting at StackOverflow's Math area (Is it different from StackOverflow Programming? How so?)

Sorry and thanks!

Also, couldn't find the right tag.. Sorry!

Answer 1

$$\frac{105}{55} = 1 + \frac{50}{55}$$

how should I convert the remainder to a decimal?

The remainder is $\frac{50}{55}$. If you want to know HOW to convert this to a decimal, you have to do long division. It is easiest to simplify the fraction first to get $\frac{10}{11}$. Do you know long division of this kind?

$$ \qquad\quad 0.90 \\ 11\overline{)10}\\ \underline{-\quad 0}\\ \qquad 100\\ \underline{-\quad\;\;\, 99}\\ \qquad\quad\;\; 10\\ \underline{-\qquad\;\;\;\;\, 0}\\ \qquad\qquad\; 100 $$

At that point, you can see that it will start repeating as $0.909090...$

We can round that off to $0.9$ or $0.91$ or $0.909$ or $0.9091$ or to any number of digits you want. Or you can concisely write it as $0.\overline{90}$

Answer 2

$$\frac {105}{55} = 1 + \frac{50}{55} = 1+\frac {10}{11}\approx 1.91$$

Use long division of the remainder $50$ divided by divisor ($55$), or to divide $10$ by $11$ to obtain the non-integer portion of the answer. Indeed, you can simply use long division to obtain the complete decimal answer to $\dfrac {105}{55}.$ You will obtain $1.909090....$

Answer 3

You have $\frac {10.5}{5.5}=\frac {105}{55}=1+\frac {50}{55}=1+\frac {10}{11}$

The idea of a remainder is difficult when the numbers involved are not whole numbers. When it is, if you are asked for $\frac ab$, you can say $a=qb+r$ with $q$ the quotient and $r$ the remainder both whole numbers. For this case, you could say $10.5=1\cdot 5.5+5.0$ so the quotient is $1$ and the remainder is $5$, but if you were asked for $\frac {10.4}{5.5}$ you would get quotient $1$ and remainder $4.9$. This is true mathematically, but probably not very useful.