Decimal fraction remainder

🏆Practice decimal fractions' meaning

Decimal remainder

A decimal remainder or decimal fraction is everything that appears to the right of the decimal point.
When the whole number is 00, the entire number (not just what appears to the right of the decimal point) is the remainder.

Mathematical concept of division showing the whole number and remainder. Visual representation to explain quotient and remainder in long division. Fundamental arithmetic concept

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Determine the number of hundredths in the following number:

0.96

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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.

How do we identify a remainder in a decimal fraction or decimal number?

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:

Mathematical concept of division showing the whole number and remainder. Visual representation to explain quotient and remainder in long division. Fundamental arithmetic concept

Let's look at an example:
What is the decimal remainder in:
45.645.6

The answer is remainder 66.
It can also be written as: 0.60.6

Another example:
What is the remainder in the number 8.4498.449
The answer is 449449 or 0.4490.449

Pay attention -
If you see the decimal number 45.0645.06 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 45.0645.06
the remainder is 0.060.06 and not 66 or 0.60.6
*Even though it's just a digit of 00, it is significant when dealing with remainders.


Important note:
When we have a decimal number where the whole number part is 00, meaning it has no whole numbers,
the entire number is actually a remainder, because there are no whole numbers.

For example –
In the number: 0.50.5
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 55 cake slices among 44 children.
Each child will get one slice and a quarter of a slice.
So the remainder is 141 \over 4
But what happens if we want to divide 11 slice between 22 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 00?
When there are no digits after the decimal point, we can determine that the remainder is 00 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 1212?
There is no remainder.
And now?
12.0000012.00000?
Still no remainder, remainder 00.


Special cases:
We said that when a number appears to the right of the decimal point like 6.56.5 we can determine that the remainder is 55 or 0.50.5.
But what happens with a decimal number like 67.000367.0003?
In this case, the remainder is not 33 but 0.00030.0003
It's important that we write 00 and then a decimal point to understand the meaning of .0003.0003
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 87.287.2?
Solution:0.2 0.2

What is the decimal remainder in 12.1212.12?
Solution:
Since both the remainder is 1212 and the whole number is 1212, it is highly recommended to add a decimal point and the digit 00 on the left to emphasize that this is a remainder.
Therefore, the remainder in this number is 0.120.12

What is the remainder in the number 2323?
Solution: There is no remainder. If there was a decimal point, there would only be 00 to its right.

What is the decimal part in the number 55.000555.00055?

Solution: Note,
if you write 5555 it would be a complete mistake since there are several zeros before 5555 .
Therefore, the answer is 0.000550.00055

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Examples with solutions for Decimal Fractions' Meaning

Exercise #1

Which figure represents 0.1?

Step-by-Step Solution

The task is to determine which of the given figures correctly represents the decimal fraction 0.1.

To interpret 0.1, we recognize it as 110\frac{1}{10}. This indicates that in a graphical representation of 10 equal parts, 1 part should be shaded. Each figure is assumed to be divided into such equal parts.

Let's analyze the options:

  • Choice 1: Shows 10 equal divisions with 1 part shaded. This potentially represents 0.1 since it shades exactly 1 of 10 parts.
  • Choice 2: Shows 10 equal divisions with more than 1 part shaded. Thus, it represents more than 0.1.
  • Choice 3: Shows 10 equal divisions with numerous parts shaded. It represents a number greater than 0.1.
  • Choice 4: Shows a full shading, representing 1 (i.e., shading all 10 parts), clearly not 0.1.

Hence, the correct choice that correspond to 0.1 is Choice 1. This figure accurately shades exactly 1 out of 10 equal segments.

Therefore, the solution to the problem indicates that choice 1 correctly represents the decimal fraction 0.1.

Answer

Exercise #2

Which figure represents seven tenths?

Step-by-Step Solution

To solve the problem of identifying which figure represents seven tenths, follow these steps:

  • Step 1: Understand that the problem requires identification of a geometric representation for the fraction 710\frac{7}{10} or decimal 0.7.
  • Step 2: Each figure is divided into ten equal segments, representing one tenth each.
  • Step 3: Carefully count the number of segments filled or shaded in each figure.

Now, let's apply these steps:

Step 1: We note that each figure is evenly divided into ten parts.

Step 2: By inspecting each option, you can see which has exactly seven segments shaded. This corresponds directly to seven out of ten segments, or seven tenths.

Step 3: Upon review, the figure corresponding to choice 3 shows exactly seven shaded segments out of ten.

Therefore, the solution to the problem is eminently found as choice 3, representing seven tenths.

Answer

Exercise #3

Determine the numerical value of the shaded area:

Step-by-Step Solution

To solve this problem, let's analyze the shaded area in terms of grid squares:

  • Step 1: The top rectangle in the grid is completely filled. Let's count the shaded squares horizontally: There are 10 squares across aligned vertically in 1 row, giving 11 as the shaded area.
  • Step 2: The bottom rectangle is partially filled. Observe it spans 66 squares horizontally by 11 square height in the grid row. The shaded area will, therefore, be 0.60.6 as it spans only 60%60\% of the horizontal extent.
  • Step 3: Add both shaded areas of the rectangles from step 1 and step 2: 11 (top) and 0.60.6 (bottom).

Thus, the total shaded area is 1+0.6=1.61 + 0.6 = 1.6.

Therefore, the solution to the problem is 1.61.6.

Answer

1.6

Exercise #4

Determine the number of ones in the following number:

0.73

Video Solution

Step-by-Step Solution

To solve this problem, let's carefully examine the decimal number 0.73 0.73 digit by digit:

  • The first digit after the decimal point is 7 7 .
  • The second digit after the decimal point is 3 3 .

We observe that there are no digits in the sequence of 0.73 0.73 that are the number '1'. Therefore, there are no '1's in the decimal number 0.73 0.73 .

Thus, the number of ones in the number 0.73 0.73 is 0.

The correct choice, given the options, is choice id 1: 0.

Answer

0

Exercise #5

Determine the numerical value of the shaded area:

Step-by-Step Solution

To solve this problem, let's follow the outlined plan:

  • Step 1: Count the number of shaded sections.
  • Step 2: Count the total number of sections in the rectangle.
  • Step 3: Express the number of shaded sections as a fraction of the total sections.
  • Step 4: Convert this fraction to a decimal to find the numerical value.

Now, let's apply these steps:
Step 1: The given diagram shows that there are 4 vertical stripes shaded.
Step 2: The total number of vertical stripes (including both shaded and unshaded) is 10.
Step 3: The fraction of shaded area is 410\frac{4}{10}.
Step 4: Convert 410\frac{4}{10} to a decimal. This equals 0.40.4.

Therefore, the numerical value of the shaded area is 0.4.

Answer

0.4

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