A Basic Guide to Decimals
2026-02-21 20:24 Diff
https://brightchamps.com/en-us/math/numbers/decimals

1783 Learners

Last updated on November 14, 2025

Have you ever used money ₹10.50 or measured something as 2.5 cm? That’s a decimal. Decimals help us show whole numbers and fractions together. They are used in calculations, measurements, and money. Let’s learn more about them.

What are Decimals in Math?

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

Decimals are numbers that show both whole numbers and parts of a whole. They are written with a decimal point. For example, if a cake costs 5 dollars and 25 cents, we write it as $5.25 where 5 is the whole number and 25 is the fractional part.
 

Decimals are another way to write fractions. You can easily change a decimal to a fraction or a fraction to a decimal. For example, \(\frac{3}{8}\) as a decimal is 0.375, and \(\frac{1}{8}\) as a decimal is 0.125. Learning how to convert decimals to fractions helps in solving problems faster.
 

Decimals are used in daily life in money, measurements, and even in computers. In computers, we change binary to decimal or hexadecimal to decimal. Knowing decimal place value and decimal places helps us write and round numbers correctly.
 

There are two types of decimals terminating decimals (that end, like 0.5) and non-terminating decimals (that go on forever, like 0.333…).
 

You can also use a decimal calculator to change decimal to percent or percent to decimal easily.
 

Decimals have a long history. The idea of zero came from the Indian mathematician Aryabhata, which helped form modern decimals. Later, Simon Stevin and John Napier made decimals popular in math.
 

Properties of Decimals

Decimals are a set of numbers that express both whole numbers and fractional parts. They play a vital role in everyday calculations to scientific operations. Several properties that make decimals a convenient way to represent numbers are listed below:
 

  • Placing decimal in multiplication: When we add or subtract decimals, we should align the decimal points correctly. For example, 13.56 + 9.5 = 23.06. When multiplying decimals, we multiply them as whole numbers and then place the decimal point based on the total decimal places. For example, 3.5 × 1.4 = 4.9.
  • Dividing decimals: To divide decimals, we shift the decimal point to make the divisor a whole number. For example, 4.0 ÷ 0.2 = 20. We can also use a decimal calculator for quick answers. Between two decimals like 0.1 and 0.2, there are more decimals, such as 0.15 and 0.17.
  • Decimal fraction conversion: Decimals can be changed into fractions and vice versa. To convert a decimal to a fraction, write it over its place value; for example, 0.25 = \(\frac{1}{4}\). To convert a fraction to a decimal, divide the numerator by the denominator; for example, \(\frac{3}{8}\) as a decimal is 0.375 and \(\frac{1}{8}\) as a decimal is 0.125.
  • Decimal percent conversion: Decimals can also be written as percentages. To convert decimal to percent, multiply by 100 (0.75 = 75%), and to convert percent to decimal, divide by 100 (45% = 0.45). In computers, numbers are also written in binary, hex, and decimal forms. We can change binary to decimal or hexadecimal to decimal easily using conversion methods.
  • Understanding terminating decimals: Some decimals stop after a few digits, they are called terminating decimals. For example, 1/4 = 0.25 is a terminating decimal.

Classification of Decimals

Decimals are divided into three main types based on the numbers that appear after the decimal point: terminating decimals, non-terminating decimals, and recurring decimals. Understanding these categories helps us easily convert between decimals and fractions.
 

  • Terminating decimals
    Terminating decimals are those that stop after a few digits. They have a fixed number of decimal places, and division by them gives no remainder. For example, 0.25 is a terminating decimal because it ends after two digits. You can convert this decimal to a fraction as 0.25 = \(\frac{25}{100}\) = \(\frac{1}{4}\). Similarly, \(\frac{1}{8}\) as a decimal is 0.125 and \(\frac{3}{8}\) as a decimal is 0.375 both are terminating decimals.
     
  • Non-Terminating decimals
    Non-terminating decimals go on endlessly after the decimal point. They have an infinite number of digits. Some of them follow a pattern, while others don’t. For example, 0.5555... continues forever, so it is a non-terminating decimal. When these decimals repeat, they are known as recurring decimals.
  • Recurring decimals
    Recurring decimals are non-terminating decimals with repeating digits or groups of digits. For instance, 1.6777... repeats the digit 7 infinitely. These decimals can also be written as fractions. For example, \(\frac{1}{3}\)= 0.3333... and \(\frac{1}{7}\) = 0.142857142857....

Explore Our Programs

Types of Decimals

Here, understanding the different types of decimals helps students solve math problems more easily. The two most common types are pure decimals and mixed decimals.

  • Pure decimal
    Pure decimals are numbers that have digits only after the decimal point, without any whole number part. Their value is always less than 1. These decimals are often used to represent fractions. For example, 0.5, 0.25, 0.0089.
  • Mixed decimals
    Mixed decimals are numbers that include both a whole number part and a fractional part, separated by a decimal point. The digits to the left of the point are whole numbers, while those on the right represent fractions. For example, 3.67, 11.42, 540.9

Importance of Decimals for Students

Decimals are an essential part of both learning and daily life.
They help students develop accuracy, precision, and problem-solving skills in academics and real-world applications.
 

  • Decimals help us get accurate results in both everyday calculations and academic concepts.
     
  • They are essential in daily life when dealing with money, weight, and length, where whole numbers alone cannot give exact values. For example, a weighing machine may show 52.6 kg instead of 52 kg, decimals help us read the same measurement.
  • In higher-level math topics such as algebra, percentages, and ratios, understanding decimals is essential for solving problems correctly.
  • Students who understand decimals well can perform better at science, engineering, technology, computer programming, and coding.
  • Decimals play a key role in achieving accuracy and precision in both academic learning and real-world applications.

Tips and Tricks to Master Decimals

To solve mathematical problems effectively, we need to understand some tips and tricks. Here are some valuable tips and tricks for kids to learn more about decimals. 
 

  • Always remember the place values of decimal digits. The values of digits, after the decimal point, are such as tenths, hundredths, thousandths, and so on. 
  • Align the decimal points when adding or subtracting numbers.
  • When we multiply, overlook the decimal point and multiply it as a whole number. After that, apply the point to the result.
  • If some numbers have fewer place values, add leading zeroes to make calculations straightforward.
     

  • When dividing decimals, if the divisor is not a whole number, multiply both the divisor and dividend by the same power of 10 to make the divisor a whole number, then perform the division as usual, placing the decimal point correctly in the quotient.
     

  • Use visual aids such as charts and decimal grids, and introduce simple conversions, such as fraction-to-decimal and decimal-to-fraction, to strengthen understanding.
     

  • Parents can encourage children to relate decimals to everyday situations, such as measuring ingredients, reading price tags, and converting percentages to decimals and vice versa while shopping.

Real-World Applications of Decimals

In our everyday life, decimals play an essential role in ensuring accuracy and precision. Whether it’s checking our weight, calculating distance, or handling money, decimals are everywhere around us. Here are some real-life applications of decimals:
 

  • In our daily life, prices in shops and banks are written in decimal form, such as ₹8.55. Even interest rates for loans and savings are often shown in decimals, like 1.7%.
  • When measuring body weight, we often see decimal values for accuracy, for example, 65.4 kg. Similarly, the lengths of various objects are recorded in decimal form, such as 2.75 meters.
  • Distances are usually measured with decimal precision. For example, the distance between two places can be 5.8 km instead of a whole number.
  • In science, decimals are used in calculations to ensure accurate, precise results.
  • Decimal values also play a key role in measuring time, for example, an athlete completing a race in 7.65 seconds.

Common Mistakes and How to Avoid Them in Decimals

Students make mistakes while dealing with decimals. If students get confused about decimals and mistakenly calculate the values, it will lead to wrong results. Here are some common errors and helpful solutions to avoid those to make the right answers. 
 

Download Worksheets

Problem 1

Add 5.35 and 3.2

Okay, lets begin

We can find the sum of both numbers by adding zero to the number that has fewer place values.
5.35 + 3.20 = 8.55
 

Explanation

The sum of 5.35 and 3.2 is 8.55. If a number has a fewer place value, we can add zeros and make the calculation simpler and easier. 
 

Well explained 👍

Problem 2

Samuel runs 2.4 kilometers per day. He wants to know how many kilometers he runs in a week. Calculate the total kilometers he runs in a week.

Okay, lets begin

 To find the answer, we can multiply the given number by the total number of days. 

The total distance Samuel runs = 2.4 × 7 

When we multiply decimal numbers, we ignore the decimal point, and then multiply it. After finding the answer, we apply the decimal point to the result. 

\(24 × 7 = 168\)

Now, we can apply the decimal point to the 168. In 2.4, there is only one decimal place. So, the final result is 16.8
 

Explanation

 Samuel runs 2.4 km every day. Within a week, he runs a total of 16.8 km. 
 

Well explained 👍

Problem 3

In a bank, there are 2 types of loans. The first loan’s interest rate is 1.5%, and the second loan’s interest rate is 2.7%. If a client took both loans, how much total interest rate does he need to pay?

Okay, lets begin

 The client has to pay a total of 4.2% of interest for both loans
 

Explanation

 Let us calculate the total interest rate by adding two interest rates. 

First loan = 1.5%

Second loan = 2.7%

Now we can add these two interest rates:

1.5% + 2.7% = 4.2%

The total interest rate the client needs to pay is the sum of both interest rates.  
 

Well explained 👍

Problem 4

Mary has a height of 5.67 feet. Her friend Siya has a height of 7.6 feet. How much taller is Siya than Mary?

Okay, lets begin

To know how much taller Siya is than Mary, we have to subtract the heights of both girls.

Height of Mary = 5.67 feet 

Height of Siya = 7.6 feet

Now, let us align the decimal points, and then we can subtract:

7.60 – 5.67 = 1.93 feet 
 

Explanation

The difference between both of their heights is 1.93 feet. Hence, Siya is 1.93 feet taller than Mary. 
 

Well explained 👍

Problem 5

Class A is conducting a trip to Kashmir. The total cost of the picnic is $15,000. There are 17 students in the class. How much does each student need to pay?

Okay, lets begin

We need to divide the total cost of the trip by the total number of students.

Total cost =  $15,000

Number of students = 17

Let us divide the given numbers:

15000 ÷ 17 = $882.353
 

Explanation

Each student needs to pay an amount of $882.353 for the trip. If 17 students pay $882.353, the total amount will be $15,000. 

Well explained 👍

FAQs on Decimals

1.What do you mean by decimal?

Decimals are used to represent numbers that have both an integer part and also a fractional part. For example, 3.67 is a decimal number, where 3 is the integer part and 67 is the fractional part. A decimal point separates both parts. 
 

2. Explain terminating decimals.

After the decimal point, terminating decimals have a finite number of digits. These digits end or terminate after a certain point, and they do not repeat. For instance, 0.34, 1.76, and 5.12 are some examples of terminating decimals.
 

3.How do we find pure decimals?

The value of pure decimals will be less than 1. Pure decimals refer to the decimals which have digits only after the decimal point. These decimals do not have a whole number, just the fractional part. For example, 0.4, 0.87, and 0.98 are the examples of pure decimals. 
 

4. What are the criteria for multiplying decimals?

While multiplying decimals, overlook the decimal points and then multiply them as whole numbers. After multiplying, apply the decimal point to the final results by counting the decimal places of the given decimals. 
 

5. How to find the place value of decimals?

In a decimal number, a decimal point divides the whole number and the fractional part. The value of numbers placed on the left side of the decimal point such as ones, tens, hundreds, and so on. The values of right-side numbers are tenths, hundredths, and so on. For example, in 1.35, 1 is in the ones place, 3 is in the tenths place, and 5 is in the hundredths place.
 

6.How to pronounce decimal numbers?

When we speak about a decimal number, the digits after the decimal point stand independently. For instance, 14.876 is a decimal number. Here, it is pronounced as fourteen point eight seven six. We do not count 876 as eight hundred and seventy-six. 
 

7.How can we round a decimal?

If we want to round a decimal, look at the digits after the decimal points. If the last digit is 5 or greater than 5, round up the digits on its left side. If the last digit is less than 5, round down.
For example, 
 2. 458 can be rounded up to 2.46
 

8.Is 0.12 greater than 0.2?

No, 0.2 is the greatest number. When we compare these decimals, 0.12 means 12 out of 100. Whereas, 0.2 means 20 out of 100. Hence, 0.2 is greater than 0.12.
 

9.How do you define fractions and decimals?

Decimals are used to represent whole numbers and fractions using powers of 10. While fractions are a part of a whole. It can be written as a ratio. For example, 3.56 is a decimal number whereas, ¼ is a fraction. 
 

10.What is the real-life significance of decimals?

In our daily lives, decimals are commonly used to express precise results. When we are dealing with financial transactions, the amount is written in decimal form. Decimals are used to explain the weight and height of objects or anything else. The real-life applications of decimal numbers are numerous. 
 

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.