A decimal number is a number used to represent a whole quantity, part of a whole, or a combination of both. Decimal numbers are based on the base-10 number system, which uses the digits 0 through 9. A decimal point separates the whole-number part from the fractional part.
For example, consider:
15.75
Here, 15 is the whole-number part, the dot (.) is the decimal point, and 75 represents the fractional part.
Decimals are common in mathematics and everyday life. We use them when working with money, measurements, percentages, scientific values, distances, weights, and many other quantities. Learning decimal place value is the key to understanding how decimal numbers work.
What Is a Decimal Number?
A decimal number is a way of writing numbers using decimal notation. It can contain a decimal point that separates whole units from parts smaller than one.
Examples include:
- 0.5
- 1.25
- 7.8
- 12.45
- 105.007
Consider 4.6.
The digit 4 represents four whole units, while 6 represents six tenths. Therefore:
4.6 = 4 + 6/10
Similarly:
2.35 = 2 + 3/10 + 5/100
Understanding these place values makes decimal numbers much easier to read, compare and calculate.
What Is a Decimal Point?
The decimal point is the dot used to separate the whole-number part of a decimal from its fractional part.
For example:
28.64
The decimal point separates 28 from 64.
Digits to the left of the decimal point represent whole-number place values such as ones, tens and hundreds. Digits to the right represent fractional place values such as tenths, hundredths and thousandths.
The position of each digit is important because changing its position changes its value.
For example:
0.5 = five tenths
but:
0.05 = five hundredths
Therefore, 0.5 and 0.05 do not have the same value.
Understanding Decimal Place Value
The place value of a digit tells us how much that digit represents according to its position.
Consider the number:
326.475
Its place values are:
| Digit | Place | Value |
| 3 | Hundreds | 300 |
| 2 | Tens | 20 |
| 6 | Ones | 6 |
| 4 | Tenths | 0.4 |
| 7 | Hundredths | 0.07 |
| 5 | Thousandths | 0.005 |
So we can write:
326.475 = 300 + 20 + 6 + 0.4 + 0.07 + 0.005
Notice an important pattern: as we move one place to the right, each place value becomes one-tenth of the place before it.
Tenths
The first position after the decimal point is the tenths place.
For example:
0.7 = 7/10
So 0.7 means seven tenths.
Hundredths
The second position after the decimal point is the hundredths place.
For example:
0.07 = 7/100
Similarly:
0.25 = 25/100
Thousandths
The third position after the decimal point is the thousandths place.
For example:
0.007 = 7/1000
In the number 3.456, the digit 4 represents four tenths, 5 represents five hundredths, and 6 represents six thousandths.
Decimal Numbers and Fractions
Decimals and fractions are two different ways of representing parts of a whole.
For example:
0.5 = 5/10 = 1/2
Similarly:
0.25 = 25/100 = 1/4
And:
0.75 = 75/100 = 3/4
The place value of the final decimal digit helps determine the denominator when converting a terminating decimal into a fraction.
For example:
0.8 = 8/10
Because there is one decimal place.
For 0.36, there are two decimal places:
0.36 = 36/100 = 9/25
For 0.125, there are three decimal places:
0.125 = 125/1000 = 1/8
After writing the fraction, simplify it when possible.
Types of Decimal Numbers
Decimal numbers can be classified according to how their digits behave after the decimal point.
Terminating Decimal
A terminating decimal has a finite number of digits after the decimal point.
Examples include:
0.5, 1.25, 3.875, 10.04
The digits eventually stop.
For example:
1/4 = 0.25
Since 0.25 has only two digits after the decimal point, it is a terminating decimal.
Repeating Decimal
A repeating decimal has a digit or sequence of digits that repeats indefinitely.
For example:
1/3 = 0.333…
The digit 3 continues forever.
Another example is:
2/3 = 0.666…
Repeating decimals are also called recurring decimals in some mathematics courses.
How to Compare Decimal Numbers
When comparing decimals, compare digits according to their place values.
Suppose we want to compare:
4.72 and 4.68
First compare the whole-number parts:
4 = 4
Next compare the tenths:
7 > 6
Therefore:
4.72 > 4.68
Adding zeros to the right can also make comparisons easier without changing the value.
For example:
0.8 = 0.80
Now compare:
0.80 and 0.75
Since 80 hundredths is greater than 75 hundredths:
0.8 > 0.75
This prevents the common mistake of assuming that the number with more decimal digits must be larger.
How to Round Decimal Numbers
Rounding gives an approximate value that is easier to use.
Suppose we want to round:
6.47
to the nearest tenth.
The tenths digit is 4. Look at the next digit, which is 7.
Because 7 is 5 or greater, increase the tenths digit by one:
6.47 ≈ 6.5
Now consider:
8.23
rounded to the nearest tenth.
The hundredths digit is 3. Because 3 is less than 5, the tenths digit stays unchanged:
8.23 ≈ 8.2
A simple rule is:
- If the next digit is 0–4, keep the rounding digit unchanged.
- If the next digit is 5–9, increase the rounding digit by 1.
Adding Decimal Numbers
When adding decimals, the most important step is to align the decimal points.
Example:
12.35 + 4.20
Write the numbers so their decimal points line up:
12.35 + 4.20 = 16.55
Another example:
5.7 + 2.45
You can write 5.7 as 5.70:
5.70 + 2.45 = 8.15
Adding a zero at the end of a decimal does not change its value.
Subtracting Decimal Numbers
Decimal subtraction follows the same principle: align the decimal points before subtracting.
Example:
9.75 − 3.20 = 6.55
Consider another example:
10.0 − 2.65
Write 10.0 as 10.00:
10.00 − 2.65 = 7.35
Using placeholder zeros can make decimal subtraction clearer and reduce errors.
Multiplying Decimal Numbers
When multiplying decimals, first multiply the numbers as though there were no decimal points. Then place the decimal point in the answer according to the total number of decimal places in the factors.
Example:
1.2 × 0.5
Ignoring the decimal points:
12 × 5 = 60
There are two decimal places altogether, so:
1.2 × 0.5 = 0.60 = 0.6
Understanding place value is important because an incorrectly positioned decimal point can produce a very different answer.
Dividing Decimal Numbers
Decimal division can often be made easier by changing the divisor into a whole number.
For example:
4.8 ÷ 0.6
Multiply both numbers by 10:
48 ÷ 6 = 8
Therefore:
4.8 ÷ 0.6 = 8
The key is to move the decimal point by the same number of places in both the dividend and divisor so that the value of the division does not change.
Decimals and Percentages
Decimals are closely connected to percentages.
To convert a decimal to a percentage, multiply by 100 and add the percent symbol.
For example:
0.5 × 100 = 50%
Therefore:
0.5 = 50%
Similarly:
0.25 = 25%
0.75 = 75%
1.25 = 125%
To convert a percentage to a decimal, divide by 100.
For example:
35% = 35 ÷ 100 = 0.35
Understanding this relationship is useful when solving problems involving discounts, marks, statistics and proportions.
Decimal Numbers in Everyday Life
Decimal numbers are not limited to classroom exercises. They are used whenever quantities need to be represented more precisely than whole numbers alone allow.
For example, a measurement might be written as 2.5 metres, while a student’s calculation might produce 7.25.
Money is another familiar example. An amount such as Rs. 125.50 contains a whole-number amount and a fractional part of a rupee.
Decimals are also commonly used in measurements involving length, mass, temperature, science and numerical data.
Common Mistakes to Avoid
1. Ignoring Place Value
Students sometimes treat every digit after the decimal point as having the same value.
For example:
0.5 ≠ 0.05
The first number represents five tenths, while the second represents five hundredths.
2. Assuming More Digits Means a Larger Number
Consider:
0.9 and 0.85
Although 0.85 contains more digits, we can write:
0.9 = 0.90
Therefore:
0.90 > 0.85
So:
0.9 > 0.85
3. Not Aligning Decimal Points
When adding:
2.5 + 1.25
write 2.5 as 2.50 and align the decimal points:
2.50 + 1.25 = 3.75
4. Confusing Tenths and Hundredths
Remember:
0.4 = 4/10
while:
0.04 = 4/100
Their positions determine their values.
Easy Way to Learn Decimal Numbers
Start by mastering place value rather than memorizing separate decimal rules.
First learn:
ones → tenths → hundredths → thousandths
Then practise reading numbers aloud.
For example:
4.25 = four and twenty-five hundredths
Next, connect decimals with familiar fractions:
0.5 = 1/2
0.25 = 1/4
0.75 = 3/4
Finally, practise comparing, rounding and performing operations with decimals. A place-value chart or number line can make these relationships easier to see.
Key Takeaways
- A decimal number represents whole quantities, fractional quantities, or both.
- The decimal point separates the whole-number and fractional parts.
- The first three decimal places are tenths, hundredths and thousandths.
- Decimal numbers can represent fractions and percentages.
- Terminating decimals end, while repeating decimals continue in a repeating pattern.
- Compare decimals according to place value, not simply by the number of digits.
- Align decimal points when adding and subtracting decimals.
- Place value is the foundation for understanding decimal calculations.
Conclusion
Decimal numbers become much easier once you understand place value. The decimal point separates whole units from fractional parts, while each position to its right represents tenths, hundredths, thousandths and increasingly smaller values.
Students should first become comfortable reading and identifying decimal places before moving to comparing, rounding, adding, subtracting, multiplying and dividing decimals. Connecting decimals with fractions and percentages can also make the concept easier to understand.
Continue learning with Digital Libraries by exploring related guides on fractions, percentages, place value and the number system, then test your understanding with decimal practice questions.
FAQ
What is a decimal number in simple words?
A decimal number is a number that can show whole units and parts of a whole using decimal notation. For example, 2.5 represents two whole units and five tenths.
What are the first three decimal places?
The first three places to the right of the decimal point are tenths, hundredths and thousandths.
What is the difference between 0.5 and 0.05?
0.5 represents five tenths, while 0.05 represents five hundredths. Therefore, 0.5 is greater than 0.05.
Can a decimal be converted into a fraction?
Yes. A terminating decimal can be written as a fraction using its place value. For example, 0.75 = 75/100 = 3/4.
What is the difference between terminating and repeating decimals?
A terminating decimal has a finite number of decimal digits, such as 0.25. A repeating decimal has a digit or group of digits that repeats indefinitely, such as 0.333….
How can students become better at decimals?
Start with place value, connect common decimals to fractions, use number lines or place-value charts, and then practise comparing, rounding and performing arithmetic operations with decimals.