Decimal Fractions

Decimal Numbers

Meaning of the Decimal Number

The decimal number represents, through the decimal point (or comma in certain countries), a simple fraction or a number that is not whole.
The decimal point divides the number in the following way:

Detailed explanation

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Test yourself on decimal fractions - advanced!

Determine the number of tenths in the following number:

1.3

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Reduction and Amplification of Decimal Numbers

Amplification of Decimal Numbers
We will add the digit $0$ to the end of the decimal number (to the right), and thus, the value of the decimal number will not change.
Reduction of Decimal Numbers
If the digit in the far-right position is $0$ , we will remove it and the value of the decimal number will not change.

Addition and Subtraction of Decimal Numbers

We will solve these operations vertically keeping in mind the following rules:
• We will take into account the rules of addition and subtraction of integers.
• Decimal points must always be positioned one below the other.
• We will write the numbers in an orderly manner - both to the right of the decimal point and to its left. (tenths below tenths, hundredths below hundredths, and so on)

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Test your knowledge

Question 1

Determine the number of ones in the following number:

0.4

Question 2

Determine the number of ones in the following number:

0.07

Question 3

Determine the number of hundredths in the following number:

0.96

Comparison of Decimal Numbers

First step:
We will control the whole parts - the decimal number with the largest whole number will be the largest of them.
Second step:
In case the whole numbers are identical we will check the digits that appear after the point.
We will go digit by digit (starting with the tenths, then hundredths, and so on)
If they continue to be equal, we proceed with the comparison of the following ones.
If they are different, we can determine which number is the largest.

Conversion of Decimal Number to Fraction

Let's see how to read the fraction
If we use the word tenths, we will place $10$ in the denominator
If we use the word hundredths, we will place $100$ in the denominator
If we use the word thousandths, we will place $1000$ in the denominator.

We will place the number itself in the numerator.
*If the integer figure differs from $0$ , we will note it next to the simple fraction.

Do you know what the answer is?

Question 1

Determine the number of ones in the following number:

0.81

Question 2

Write the following decimal fraction as a simple fraction and simplify:

$$ 0.36= $$

Question 3

Write the following decimal fraction as a simple fraction and simplify:

$$ 0.5= $$

Conversion from Decimal Number to Mixed Number

First, we will convert the decimal number to a fraction according to the rules.
Then, we will convert the simple fraction to a mixed number using the following method:
We will calculate how many whole times the numerator fits into the denominator - this will be the whole number.
What remains, we will write in the numerator, and the denominator will remain unchanged (does not change).

Multiplication and Division of Decimal Numbers by 10, 100, etc.

In multiplications: we will slide the decimal point to the right as many steps as the number has zeros.
In divisions: we will slide the decimal point to the left as many steps as the number has zeros.

Check your understanding

Question 1

Write the following decimal fraction as a simple fraction and simplify:

$$ 0.350 $$

Question 2

Write the following decimal fraction as a simple fraction and simplify:

$$ 0.630 $$

Question 3

$$ 0.75+0.35= $$

Multiplication of Decimal Numbers

We will solve using the vertical multiplication method according to the following steps:
*We will write the numbers neatly one under the other, including the decimal points, one under the other, tenths under tenths, hundredths under hundredths, etc.
*We will solve the exercise, for now, we will not pay attention to the decimal point and will only act according to the rules of vertical multiplication.
*We will review each number in the exercise and count how many digits there are after the decimal point.
We will add up the total number of digits that are after the decimal point (taking into account both numbers) and that will be the number of digits that will be after the decimal point in the final answer.

Division of Decimal Numbers

We will proceed in the following order:
First step -> We will make the decimal point in the dividend (the number we want to divide) disappear, moving it to the right the necessary number of places until it is completely gone.
Second step -> In the divisor (the second number in the operation, that is, the number by which it is divided) we will move the decimal point to the right the same number of places that we moved in the first number (even if this number of steps is not enough to make it disappear)
Third step -> We will solve the "new" exercise (with the "new" numbers).

Do you think you will be able to solve it?

Question 1

Determine the number of tenths in the following number:

0.96

Question 2

Determine the number of ones in the following number:

0.73

Question 3

$$ 2.6:0.1= $$

Repeating Decimal

A repeating decimal is a number with a fractional part that, after the decimal point, the digits repeat infinitely, in a periodic manner.
To learn how to convert a fraction to a repeating decimal, consult the complete article on this topic.

Decimal Measurements

To equalize decimal measures, we will proceed as follows:
We will identify the largest unit of measure between the two numbers, convert the number with the smaller unit of measure to the larger unit of measure, and compare both numbers that now have the same unit of measure.

Test your knowledge

Question 1

Write the following decimal fraction as a simple fraction and simplify:

$$ 0.8 $$

Question 2

Write the following decimal fraction as a simple fraction and simplify:

$$ 0.58 $$

Question 3

Determine the number of tenths in the following number:

1.3

Density

Between any pair of numbers, there is an infinite number of other numbers.

Examples and exercises with solutions on decimal fractions

Exercise #1

Determine the number of tenths in the following number:

1.3

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Understand the problem of finding the number of tenths in 1.3.
Step 2: Note that the decimal number 1.3 is composed of the whole number 1 and the decimal fraction 0.3.
Step 3: Recognize that the tenths place is the first digit after the decimal point.

Now, let's work through each step:

Step 1: The problem asks us to count the number of tenths in the decimal number 1.3. This involves understanding the place value of each digit.

Step 2: In the decimal 1.3, the digit '1' represents the whole number and does not contribute to the count of tenths. The digit '3' is in the tenths place.

Step 3: Since the digit '3' is in the tenths place, it denotes 3 tenths or the fraction $\frac{3}{10}$ .

Therefore, the number of tenths in 1.3 is $3$ .

Answer

Exercise #2

Determine the number of ones in the following number:

0.4

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Examine the given number 0.4.
Identify and list all digits represented in this decimal.
Count the occurrences of the digit '1'.

Now, let's work through each step:
Step 1: The number given is 0.4. This number is composed of the digits '0', '.', and '4'.
Step 2: Identify any '1's among these digits. There are no '1's in this sequence of digits.
Step 3: Thus, the count of the digit '1' in the number 0.4 is zero.

Therefore, the number of ones in the number 0.4 is $0$ .

Answer

Exercise #3

Determine the number of ones in the following number:

0.07

Video Solution

Step-by-Step Solution

To solve this problem, we'll examine the given decimal number, $0.07$ , to identify how many '1's it contains.

Let's break down the number $0.07$ :

The digit to the left of the decimal is $0$ , which is the ones place. It is not '1'.
The first digit after the decimal point is $0$ , which represents tenths. This is also not '1'.
The next digit is $7$ , which represents hundredths. This digit is also not '1'.

None of the digits in the number $0.07$ are equal to '1'.

Therefore, the number of ones in $0.07$ is 0.

Answer

Exercise #4

Determine the number of hundredths in the following number:

0.96

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Define the place value of each digit in the decimal number.
Step 2: Identify the specific digit in the hundredths place.
Step 3: Determine the number of hundredths in 0.96.

Now, let's work through each step:

Step 1: Consider the decimal number $0.96$ . In decimal representation, the digit immediately after the decimal point represents tenths, and the digit following that represents hundredths.

Step 2: In the number $0.96$ , the digit $9$ is in the tenths place, and the digit $6$ is in the hundredths place.

Step 3: Therefore, the number of hundredths in $0.96$ is $6$ .

Thus, the solution to the problem is that there are 6 hundredths in the number $0.96$ .

Answer

Exercise #5

Determine the number of ones in the following number:

0.81

Video Solution

Step-by-Step Solution

To solve this problem, we need to examine the decimal number $0.81$ and count the number of '1's present:

The first digit after the decimal point is $8$ .
The second digit after the decimal point is $1$ .

Now, count the number of '1's in $0.81$ :

There is only one '1' in the entire number $0.81$ because it appears only once after the decimal point.

Thus, the total number of ones in $0.81$ is 0, since the task is to count ones in the whole number, and there are no ones in the integer part of $0$ , nor in the remaining digits $8$ .

Therefore, the solution to the problem is $0$ , which corresponds to choice 3.

Answer

Do you know what the answer is?

Question 1

Determine the number of ones in the following number:

0.4

Question 2

Determine the number of ones in the following number:

0.07

Question 3

Determine the number of hundredths in the following number:

0.96

Start practice

Decimal Fractions

Decimal Numbers

Meaning of the Decimal Number

Test yourself on decimal fractions - advanced!

Reduction and Amplification of Decimal Numbers

Addition and Subtraction of Decimal Numbers

Comparison of Decimal Numbers

Conversion of Decimal Number to Fraction

Conversion from Decimal Number to Mixed Number

Multiplication and Division of Decimal Numbers by 10, 100, etc.

Multiplication of Decimal Numbers

Division of Decimal Numbers

Repeating Decimal

Decimal Measurements

Density

Examples and exercises with solutions on decimal fractions

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

More Questions

All Operations in Decimal Fractions

Decimal Fractions' Meaning

Addition and Subtraction of Decimal Fractions

Reduction and Expansion of Decimal Fractions