Decimal fraction remainder

A remainder is what is left over after dividing a number that is not evenly divisible by another number, and it is essentially the part that is added to the whole.

Just to clarify - a decimal number with digits after the decimal point represents a non-whole number, meaning a fraction, and therefore can also be called a decimal fraction.

It's really easy!
A decimal number consists of a number, a decimal point, and digits to the right of the decimal point.
Everything that appears to the left of the decimal point is called the whole number.
Everything that appears to the right of the decimal point is called the decimal part.
In other words:

Let's look at an example:
What is the decimal remainder in:
$45.6$

The answer is remainder $6$.
It can also be written as: $0.6$

Another example:
What is the remainder in the number $8.449$
The answer is $449$ or $0.449$

Pay attention -
If you see the decimal number $45.06$ and were asked what the remainder is,
you need to remember that everything to the right of the decimal point is the remainder, so in the decimal number $45.06$
the remainder is $0.06$ and not $6$ or $0.6$
*Even though it's just a digit of $0$, it is significant when dealing with remainders.

Important note:
When we have a decimal number where the whole number part is $0$, meaning it has no whole numbers,
the entire number is actually a remainder, because there are no whole numbers.

For example –
In the number: $0.5$
The entire number is a remainder.
Think about it this way,
A remainder is obtained when we divide a number by another number and it doesn't divide evenly.
For example, if we divide $5$ cake slices among $4$ children.
Each child will get one slice and a quarter of a slice.
So the remainder is $1 \over 4$
But what happens if we want to divide $1$ slice between $2$ children?
Each child will get half a slice, it's not even whole and therefore the entire half is the remainder.

When will we get a remainder of $0$?
When there are no digits after the decimal point, we can determine that the remainder is $0$ or there is no remainder.
Also, if you encounter only zeros to the right of the decimal point, you can still determine there is no remainder.

Let's look at an example:
What is the remainder in the number $12$?
There is no remainder.
And now?
$12.00000$?
Still no remainder, remainder $0$.

Special cases:
We said that when a number appears to the right of the decimal point like $6.5$ we can determine that the remainder is $5$ or $0.5$.
But what happens with a decimal number like $67.0003$?
In this case, the remainder is not $3$ but $0.0003$
It's important that we write $0$ and then a decimal point to understand the meaning of $.0003$
Remember - everything that appears to the right of the decimal point is considered a remainder!

And now let's practice:
What is the decimal remainder in $87.2$?
Solution:$0.2$

What is the decimal remainder in $12.12$?
Solution:
Since both the remainder is $12$ and the whole number is $12$, it is highly recommended to add a decimal point and the digit $0$ on the left to emphasize that this is a remainder.
Therefore, the remainder in this number is $0.12$

What is the remainder in the number $23$?
Solution: There is no remainder. If there was a decimal point, there would only be $0$ to its right.

What is the decimal part in the number $55.0005$5?

Solution: Note,
if you write $55$ it would be a complete mistake since there are several zeros before $55$.
Therefore, the answer is $0.00055$