Decimal Numbers: What They Are, How to Read Them, Operations, and Exercises

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Decimal numbers allow us to represent quantities that include a whole-number part and a part smaller than one. They are fundamental for expressing measurements, prices, lengths, masses, amounts of money, and many other situations in everyday life and mathematics.

Understanding decimal numbers is not simply a matter of learning how to read them. It is also necessary to recognize the place value of each digit, compare quantities, convert fractions into decimals, and correctly perform operations such as addition, subtraction, multiplication, and division.

In this article, you will learn what decimal numbers are, how to read them, what the place value of their digits is, how to compare them, how to round them, and how to perform operations with them. You will also find examples and solved exercises to reinforce your learning.

What Are Decimal Numbers?

A decimal number is a number that can be expressed with a whole-number part and a decimal part, separated by a decimal point in the notation used in this article.

For example:

4.5 12.75 0.8 3.125

In the number 12.75, 12 represents the whole-number part, while 75 represents the decimal part.

Decimal numbers allow us to represent quantities that lie between whole numbers. For example, 4.5 lies between 4 and 5.

Key idea: The position of each digit after the decimal point determines its value.

Whole-Number Part and Decimal Part

Let us look at the number:

27.346

We can separate it into two parts:

27 | 346

Whole-number part: 27.

Decimal part: 346.

The decimal point separates the two parts. In this article, we use the period as the decimal separator to maintain consistent notation in mathematical expressions.

In Mexico and other Spanish-speaking countries, the comma is also commonly used as a decimal separator in certain contexts. What matters is recognizing that the symbol used may vary according to convention, while the mathematical value represented remains the same.

Place Value in Decimal Numbers

One of the most important ideas for understanding decimal numbers is place value. Each digit has a specific value determined by its position.

After the decimal point, the positions are, in order, tenths, hundredths, thousandths, and other decimal places.

Position	Value	Example in 5.274
Ones	1	5
Tenths	1/10	2
Hundredths	1/100	7
Thousandths	1/1000	4

Therefore, the number 5.274 can be interpreted as:

5 + 2/10 + 7/100 + 4/1000

This shows that each digit after the decimal point represents a fraction of one whole.

Tenths

The first position after the decimal point represents tenths.

For example:

0.7

It means seven tenths:

7/10

Hundredths

The second position represents hundredths.

For example:

0.25

It represents twenty-five hundredths:

25/100

Thousandths

The third position represents thousandths.

For example:

0.125

It represents one hundred twenty-five thousandths:

125/1000

How Do You Read Decimal Numbers?

Decimal numbers can be read by identifying the whole-number part and then the decimal part according to its place value.

For example:

4.5

It can be read as four and five tenths.

The number:

7.25

can be read as seven and twenty-five hundredths.

Meanwhile:

3.125

can be read as three and one hundred twenty-five thousandths.

It is also common to read a decimal by saying each digit after the decimal point. For example, 7.25 can be informally read as “seven point twenty-five.” In academic contexts, it is important to also understand its place value.

How Do You Compare Decimal Numbers?

To compare decimal numbers, we first analyze the whole-number part. If the whole-number parts are equal, we compare the decimal digits from left to right.

First Case: Different Whole-Number Parts

Compare:

5.4 and 3.9

Since 5 is greater than 3:

5.4 > 3.9

Second Case: Equal Whole-Number Parts

Compare:

4.7 and 4.3

The whole-number parts are equal. We compare the tenths: 7 is greater than 3.

4.7 > 4.3

When There Are Different Numbers of Decimal Digits

We can add zeros to the right of a decimal number without changing its value.

For example:

0.5 = 0.50 = 0.500

Therefore, to compare:

0.5 and 0.47

we can write:

0.50 > 0.47

Therefore:

0.5 > 0.47

Remember: Adding zeros to the right of the decimal part does not change the value of the number.

Decimal Fractions and Decimal Numbers

Decimal numbers are directly related to fractions whose denominators are 10, 100, 1000, or another power of 10.

For example:

0.4 = 4/10

0.25 = 25/100

0.125 = 125/1000

These equivalences explain why decimal places are called tenths, hundredths, and thousandths.

How Do You Convert a Fraction to a Decimal?

To convert a fraction into a decimal number, we can divide the numerator by the denominator.

For example:

3/4

Divide 3 by 4:

3 ÷ 4 = 0.75

Therefore:

3/4 = 0.75

Another example:

1/2 = 0.5

This relationship is important because it connects decimal numbers with rational numbers.

How Do You Add Decimal Numbers?

To add decimal numbers, we must arrange the numbers so that the decimal points are aligned. Then we add each place value from right to left, carrying when necessary.

Example:

  12.45
+  3.27
-------
  15.72

Therefore:

12.45 + 3.27 = 15.72

Aligning the decimal points is essential for avoiding place-value errors.

How Do You Subtract Decimal Numbers?

Subtraction follows a similar procedure. We must align the decimal points before performing the operation.

Example:

   8.50
−  2.35
-------
   6.15

Therefore:

8.50 − 2.35 = 6.15

It is possible to write 8.5 as 8.50 because adding a zero to the right of the decimal part does not change its value.

How Do You Multiply Decimal Numbers?

To multiply decimal numbers, we can first multiply them as if they were whole numbers and then place the decimal point by considering the total number of decimal places in the factors.

Example:

2.5 × 1.2

First, multiply 25 × 12:

25 × 12 = 300

The original factors have two decimal places in total: one in 2.5 and one in 1.2. Therefore, the result should have two decimal places:

3.00 = 3

Therefore:

2.5 × 1.2 = 3

How Do You Divide Decimal Numbers?

Division with decimal numbers requires careful attention to the position of the decimal point. When the divisor contains decimal digits, we can transform the division by multiplying both the dividend and the divisor by a power of 10 until the divisor becomes a whole number.

For example:

7.5 ÷ 2.5

Multiply both numbers by 10:

75 ÷ 25

Now perform the division:

75 ÷ 25 = 3

Therefore:

7.5 ÷ 2.5 = 3

Key idea: In a division, multiplying both the dividend and divisor by the same nonzero number does not change the quotient.

Rounding Decimal Numbers

Rounding allows us to approximate a decimal number to a specific place value.

To round a number, we look at the digit immediately to the right of the place we want to keep.

For example, let us round 4.736 to the nearest hundredth.

We want to keep:

4.73

The next digit is 6. Since 6 is greater than or equal to 5, we increase the hundredths digit by one.

4.736 ≈ 4.74

Therefore, 4.736 rounded to the nearest hundredth is 4.74.

Terminating, Repeating, and Non-Repeating Decimals

Decimal numbers can have different types of decimal expansions.

Terminating Decimal

A terminating decimal is a decimal representation that ends after a finite number of digits.

Examples:

0.5 2.75 4.125

Repeating Decimal

A repeating decimal is an infinite decimal in which a digit or group of digits repeats indefinitely.

For example:

0.333333...

This number is rational because it can be expressed as the fraction:

1/3

Infinite Non-Repeating Decimal

An infinite non-repeating decimal is a decimal that continues indefinitely without exhibiting a repeating pattern.

An example is the decimal expansion of √2:

1.41421356237...

This number is irrational.

Important: Not every infinite decimal is irrational. Infinite repeating decimals are rational; infinite non-repeating decimals are irrational.

Common Mistakes with Decimal Numbers

Not Aligning the Decimal Points

In addition and subtraction, the place values must be properly aligned.

Thinking That More Decimal Digits Always Mean a Larger Number

This is false. For example:

0.5 = 0.50

The two numbers have different numbers of digits written after the decimal point, but they represent exactly the same value.

Confusing Tenths with Hundredths

In 0.35, the 3 represents three tenths and the 5 represents five hundredths.

Forgetting Place Value

In a decimal number, changing the position of a digit changes its value. For example, the 5 in 0.5 represents five tenths, while the 5 in 0.05 represents five hundredths.

Decimal Number Exercises

Exercise 1

Identify the whole-number part and the decimal part of 18.425.

Answer: The whole-number part is 18 and the decimal part is 425.

Exercise 2

What value does the 7 represent in 3.472?

Answer: Seven hundredths, or 7/100.

Exercise 3

Compare 0.8 and 0.75.

0.8 = 0.80

0.80 > 0.75

Answer: 0.8 > 0.75.

Exercise 4

Solve:

4.35 + 2.18

4.35 + 2.18 = 6.53

Answer: 6.53.

Exercise 5

Solve:

9.20 − 3.45

9.20 − 3.45 = 5.75

Answer: 5.75.

Exercise 6

Solve:

2.4 × 1.5

2.4 × 1.5 = 3.6

Answer: 3.6.

Exercise 7

Solve:

8.4 ÷ 2.1

8.4 ÷ 2.1 = 4

Answer: 4.

Exercise 8

Convert 3/4 to a decimal.

3 ÷ 4 = 0.75

Answer: 0.75.

Frequently Asked Questions About Decimal Numbers

What Are Decimal Numbers?

They are numbers that allow us to represent a whole-number part and a fractional part using decimal notation. The digits after the decimal point represent tenths, hundredths, thousandths, and other decimal places.

What Is a Tenth?

A tenth is one-tenth of a whole and can be represented as 1/10 or 0.1.

What Is a Hundredth?

A hundredth is one-hundredth of a whole and can be represented as 1/100 or 0.01.

What Is a Thousandth?

A thousandth is one-thousandth of a whole and can be represented as 1/1000 or 0.001.

How Are Decimal Numbers Compared?

First, compare the whole-number parts. If they are equal, compare the decimal digits from left to right, beginning with the tenths.

How Are Decimal Numbers Added?

Align the decimal points and perform the addition while respecting the place value of each digit.

How Are Fractions Converted to Decimals?

Divide the numerator by the denominator. For example, 3/4 = 0.75.

Are All Decimal Numbers Rational?

Terminating decimals and infinite repeating decimals are rational. Infinite non-repeating decimals are irrational.

Conclusion

Decimal numbers are fundamental for representing quantities with greater precision than whole numbers. Understanding them begins with place value: tenths, hundredths, thousandths, and the decimal places that follow.

Learning to read and compare decimal numbers allows us to progress toward more complex operations. Addition and subtraction require particular attention to the alignment of decimal points, while multiplication and division use specific procedures related to place value.

Decimal numbers are also closely related to fractions and rational numbers. Understanding this relationship helps connect different ways of representing the same number and prepares the way for studying percentages, ratios, proportions, and other mathematical concepts.

In summary:

The value of a decimal digit depends on its position.

Zeros can be added to the right of the decimal part without changing the value of the number.

Operations with decimals require us to respect place value.

Terminating and repeating decimals belong to the set of rational numbers.

Mastering decimal numbers does not simply mean obtaining correct answers. It means understanding what each digit represents and using that information to interpret quantities and solve problems logically.

Continue Learning with Frecuencia Educativa

This topic is part of the episode:

T2E2 | Fundamentals of Arithmetic: Rational and Irrational Numbers, Fractions, Decimals, Ratios, and Proportions | Frecuencia Educativa

In this episode, you will find an integrated explanation of four fundamental topics in Arithmetic and the relationship between them.

This article explores the topic of Decimal Numbers in greater depth.

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You will be able to review place value, tenths, hundredths, thousandths, comparison, and operations with decimal numbers.

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Watch this Short, where we explain what decimal numbers are and how to identify the place value of their digits in less than one minute.

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Academic Resource Information

Collection

Mathematics

Knowledge Center

Arithmetic

Knowledge Area

Decimal Numbers

Topic

Decimal Numbers

Level

Basic

Estimated Reading Time

12–15 minutes

Resource Type

Supplementary Article

Skills Developed

Recognize the characteristics of decimal numbers.
Identify the whole-number part and the decimal part.
Understand the place value of decimal digits.
Read and compare decimal numbers.
Relate fractions to decimal representations.
Solve basic operations with decimal numbers.
Apply rounding to decimal numbers.
Distinguish between terminating, repeating, and non-repeating decimals.

Library Path

Digital Library → Mathematics Collection → Knowledge Center: Arithmetic → Knowledge Area: Decimal Numbers