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:

You can read more in the assigned extended article

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:

You can read more in the assigned extended article

Determine whether the exercise is correctly written or not.

**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.

You can read more in the assigned extended article

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)

You can read more in the assigned extended article

Test your knowledge

Question 1

Determine whether the exercise is correctly written or not.

Question 2

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds..

Question 3

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

**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.

You can read more in the assigned extended article

**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.

You can read more in the assigned extended article

Do you know what the answer is?

Question 1

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

Question 2

How much of the whole does the shaded area represent?

Question 3

How much of the whole does the shaded area represent?

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).

You can read more in the assigned extended article

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.

You can read more in the assigned extended article

Check your understanding

Question 1

How much of the whole does the shaded area represent?

Question 2

How much of the whole does the shaded (orange) area represent?

Question 3

How much of the whole does the shaded (orange) area represent?

**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.

You can read more in the assigned extended article

**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).

You can read more in the assigned extended article

Do you think you will be able to solve it?

Question 1

How much of the whole does the shaded (orange) area represent?

Question 2

\( 0.1+0.1= \)

Question 3

\( 0.2+0.1= \)

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.

You can read more in the assigned extended article

**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.

You can read more in the assigned extended article

Test your knowledge

Question 1

\( 0.2-0.1= \)

Question 2

\( 0.3-0.2= \)

Question 3

Determine whether the exercise is correctly written or not.

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

You can read more in the assigned extended article

Determine whether the exercise is correctly written or not.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Not true

Determine whether the exercise is correctly written or not.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Not true

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds..

Let's fill in the zeros in the empty space as follows:

$006.310\\+216.222\\\$We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

True

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

Let's fill in the zeros in the empty space as follows:

$21.52\\+03.40\\$

Note that the decimal points are written one below the other

Therefore, the exercise is written in the correct form

True

Write the following decimal as a fraction and simplify:

$0.75$

Since there are two digits after the decimal point, we divide 75 by 100:

$\frac{75}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 25, so:

$\frac{75:25}{100:25}=\frac{3}{4}$

$\frac{3}{4}$

Do you know what the answer is?

Question 1

Determine whether the exercise is correctly written or not.

Question 2

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds..

Question 3

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

Related Subjects

- The Order of Basic Operations: Addition, Subtraction, and Multiplication
- Order of Operations: Exponents
- Order of Operations: Roots
- Division and Fraction Bars (Vinculum)
- The Numbers 0 and 1 in Operations
- Neutral Element (Identiy Element)
- Order of Operations with Parentheses
- Order or Hierarchy of Operations with Fractions
- Opposite numbers
- Elimination of Parentheses in Real Numbers
- Addition and Subtraction of Real Numbers
- Multiplication and Division of Real Numbers
- Multiplicative Inverse
- Integer powering
- Positive and negative numbers and zero
- Real line or Numerical line
- Fractions
- A fraction as a divisor
- How do you simplify fractions?
- Simplification and Expansion of Simple Fractions
- Common denominator
- Hundredths and Thousandths
- Part of a quantity
- Mixed Numbers and Fractions Greater Than 1
- Addition and Subtraction of Mixed Numbers
- Multiplication of Integers by a Fraction and a Mixed Number
- Placing Fractions on the Number Line
- Numerator
- Denominator
- Decimal Fractions
- What is a Decimal Number?
- Reducing and Expanding Decimal Numbers
- Addition and Subtraction of Decimal Numbers
- Comparison of Decimal Numbers
- Converting Decimals to Fractions
- Multiplication and Division of Decimal Numbers by 10, 100, etc.
- Multiplication of Decimal Numbers
- Division of Decimal Numbers
- Repeating Decimal
- Decimal Measurements
- Density