Attend our in-person Robotics & Math
Decimal Numbers have significance in mathematics. They enable us to write numbers that lie between two whole numbers like 2.5, 4.75, and 8.125. Decimals might appear while working on problems based on measurement of length, monetary calculations, comparing the cost price of items, and other math problems. However, do you know about the place value after decimal?
Place Value After Decimal It refers to the position and value of digits after the decimal. The first place represents tenths, second is for hundredths, third is of thousandths, and so forth.
Consider the number 6.482; then the digit 4 is at tenths, 8 is at hundredths, and 2 is at thousandths place. Thus, knowing about the place value after decimals makes it easy for us to read, compare, and calculate decimal numbers. In this tutorial, you will learn about place value after the decimal, place value chart and some easy examples.
What Is the Place Value After Decimal?
The place value of digits after the decimal is the position of the digit which is on the right side of the decimal. Every digit after the decimal place value is the part of one whole, and the value of the digit reduces to one-tenth as we move one place to the right.
A decimal point separates the whole number from the fractional part of the number.
For instance, for 24.356
- 24 is the whole number part.
- A decimal point separates the whole number from the decimal.
- 356 is the digit which comes after the decimal point.
Each digit after the decimal point will have a different place value.
- 3 is the tenths place.
- 5 is the hundredths place.
- 6 is the thousandths place.
This means that the expansion of 24.356 will be:
24.356 = 20 + 4 + 0.3 + 0.05 + 0.006
What Comes First After the Decimal Point?
The tenths place comes first after the decimal point. The next positions are hundredths, thousandths, ten-thousandths, and so on.
Here is a quick example using the number 7.268:
- 2 is in the tenths place.
- 6 is in the hundredths place.
- 8 is in the thousandths place.
Remember this simple rule: start counting from the decimal point and move to the right.
Place Value Chart After Decimal Point
Place Value Chart After the Decimal Point
A place value chart after the decimal point helps you identify the position and value of each digit in a decimal number. It is especially useful for students who are learning decimals for the first time.
Consider the decimal number:
| Digit | Place Value | Digit's Value |
|---|---|---|
| 4 | Ones | 4 |
| 5 | Tenths | 0.5 |
| 8 | Hundredths | 0.08 |
| 2 | Thousandths | 0.002 |
In this example, the digit 4 represents four whole units. The digit 5 represents five-tenths, the digit 8 represents eight-hundredths, and the digit 2 represents two-thousandths.
Decimal Place Value Chart
Decimal Place Value Chart
Learn decimal places, their positions, and fraction forms.
| Decimal Place | Position After Decimal | Fraction Form |
|---|---|---|
| Tenths | 1st place | 1/10 |
| Hundredths | 2nd place | 1/100 |
| Thousandths | 3rd place | 1/1,000 |
| Ten-thousandths | 4th place | 1/10,000 |
| Hundred-thousandths | 5th place | 1/100,000 |
| Millionths | 6th place | 1/1,000,000 |
Math Tip: Remember Decimal Place Values
Each step to the right of the decimal point represents a smaller fraction of one whole. One-tenth is greater than one-hundredth, and one-hundredth is greater than one-thousandth.
What Are Tenths, Hundredths, and Thousandths?
Tenths, hundredths, and thousandths are the first three place values after the decimal point. Each one represents a different fraction of a whole.
1. Tenths
The tenths place is the first position after the decimal point. One tenth is equal to 1/10, or 0.1.
For example, in 5.7, the digit 7 is in the tenths place. Its value is 0.7, which means seven-tenths.
More examples:
- 2.3 = 2 + 0.3
- 6.8 = 6 + 0.8
- 9.4 = 9 + 0.4
2. Hundredths
The hundredths place is the second position after the decimal point. One hundredth is equal to 1/100, or 0.01.
For example, in 3.46, the digit 6 is in the hundredths place. Its value is 0.06, while the digit 4 represents 0.4.
Therefore:
3.46 = 3 + 0.4 + 0.06
More examples:
- 1.25 = 1 + 0.2 + 0.05
- 4.78 = 4 + 0.7 + 0.08
- 8.09 = 8 + 0.09
3. Thousandths
The thousandths place is the third position after the decimal point. One thousandth is equal to 1/1,000, or 0.001.
For example, in 7.236, the digit 6 is in the thousandths place. Its value is 0.006.
The number can be expanded as:
7.236 = 7 + 0.2 + 0.03 + 0.006
More examples:
- 2.145 = 2 + 0.1 + 0.04 + 0.005
- 5.678 = 5 + 0.6 + 0.07 + 0.008
- 9.304 = 9 + 0.3 + 0.004
Recommended Reading: How Do You Write 0.63 Repeating as a Fraction?
Conclusion
Understanding the place value after the decimal point helps you read, write, compare, and calculate decimal numbers accurately. The first position after the decimal is tenths, followed by hundredths, thousandths, and ten-thousandths. Each position represents a smaller part of a whole as you move to the right. By using a decimal place value chart and practicing examples, you can easily identify the value of each digit in a decimal number. These skills are useful in everyday situations, such as measuring lengths, handling money, and comparing prices. Keep practicing with different decimal numbers to build your confidence in mathematics.
You can opt for our Advanced Math or Vedic Math+Mental Math courses. Our Math Quiz for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.
