125 LearnersLast updated on July 23rd, 2025
Decimal Place Value
The place values of a decimal number are seen in the place value chart. Just like whole numbers have place values such as ones, tens, hundreds, and so on, decimal numbers also have their place value. Decimal place value is used to make precise calculations in measurements. Here, in this article, we will learn more about decimal place value.
What is the Decimal Place Value?
Decimal numbers have a whole number part and a fractional part. In decimal numbers, a decimal point is used to separate these parts. For example, 5.35 is a decimal number. The place value of a decimal number can be displayed using a place value chart. The place value of digits in the whole number is represented as ones, tens, hundreds, thousands, and so on. On the other hand, the place values of the fractional part are represented as tenths, hundredths, then thousandths, and so on.
How to find Decimal Place Values?
A decimal number is a type of number that has both fractional and whole number parts. For example, 6.75 is a decimal number. Here, 6 is the whole number, and the fractional part is 0.75. To find the decimal place value of a digit in a decimal number, we use a decimal place value chart. This chart helps us visually represent the place values of each digit in a number, including the digits before and after the decimal point. Here’s a chart depicting the whole number part, the decimal point, and the fractional part of a decimal number.
What is the Decimal Place value chart?
If a decimal number consists of only a whole number or just a fractional part, add zero to the part that is missing.
For example:
.85 → 0.85
32 → 32.0
Representing the place value of a number on a chart enables us to identify the positions of each digit in the number.
The fractional part of a decimal number consists of the digits that come after the decimal point.
For example, in the number 0.83, the digit 8 indicates eight-tenths, and the digit 3 indicates three-hundredths.
This can be expressed as:
0.83 = 0.8 + 0.03
Or, in fraction form:
0.83 = 8/10 + 3/100.
Real-Life Applications of Decimal Place Value
Decimals express values with accuracy in the number system. Understanding decimal place values helps us compare values more precisely. Given below are a few real-life applications of decimal place value:
- Decimal place values help in calculating discounts and taxes accurately. For example, if an item is purchased for $30.82, 8 is in the tenths place and 2 is in the hundredths place.
- Engineers ensure the measurements of materials are accurate by checking the decimal place values.
- Decimal place values are utilized in calculating the precise time in seconds or milliseconds. For example, 8.48 seconds indicates 8 whole seconds and 48 hundredths of a second.
- A vehicle’s mileage is often measured in decimals, such as 18.6 km per liter.
Common Mistakes and How to Avoid Them in Decimal Place Value
We often see children finding it difficult to learn the decimal place value, which can lead to mistakes. Given below are some of the mistakes that can be made. To overcome the mistakes, solutions are also provided. Let’s discuss them in detail:
Mistake 1
Overlooking the Role of Zero
Some students don’t know how zeros affect decimal numbers. For example, assuming 0.80 ＞0.8 or that 0.07 is equal to 0.7.
Zero that comes after a non-zero digit in a decimal place won't change. But zeros in different positions matter. For example, 0.80 and 0.8 are the same, but 0.07 is less than 0.7.
Mistake 2
Not Understanding the Place Value of Digits
They might incorrectly understand the place value of digits, which can lead to errors. For example, in the number 0.53, the digit 3 is in the tenths place instead of the hundredths place. Learn decimals using a place value chart. In the number 0.53, the digit 5 is in the tenth place, and the digit 3 is in the hundredth place.
Mistake 3
Mixing Up Decimal and Whole Number Places
Confusion between the decimal part and whole number part causes errors in their place values. For example, Students may conclude 0.7 ＞0.69 because 7 is greater than 6.
Solution: Always compare decimal numbers by identifying the place values from left to right. Here, 0.7 is equal to 0.70, so it is evident that 0.70 ＞ 0.69.
Mistake 4
Performing Arithmetic Operations Incorrectly
When performing addition or subtraction, students forget to align the decimal points accurately. For example, 1.5 + 0.66 = 1 566 (incorrect). Ensure that the numbers to be added or subtracted are aligned by their decimal point correctly before performing the operations.
Mistake 5
Errors in Rounding the Numbers
Students mistakenly round the decimal numbers like 0.58 to 0.5 instead of 0.6.
Solution: Use the rules for rounding, i.e., if the digit is equal or greater than 5, then the number will be rounded up, and if the digit is lesser than 5 then it will be rounded down.
Solved Examples of Decimal Place Values
Problem 1
Write 0.475 in expanded form.
0.475 = 0.4 + 0.07 + 0.005
Explanation
The place value of each digit in 0.475 is:
4 is in the tenth place, so we write 4/10 or 0.4
7 is in the hundredths place, so we write 7/100 or 0.07
5 is in the thousandths place, so we write 5/1000 or 0.005
Now, we need to express the number as a sum of its place values:
0.475 = 4/10 + 7/100 + 5/1000
0.4 + 0.07 + 0.005
Problem 2
Determine which is greater: 0. 83 or 0.803.
0.83 is greater than 0.803.
Explanation
The first step is to compare the digits place by place from left to right:
Tenth place→ Since both numbers consist of 8, we move to the next place.
Hundredths place → In the number 0.83:
3 is in the hundredths place.
0 is in the hundredths place. (since 3 ＞0, 0.83 is greater).
To finalize the place value, express 0.83 as 0.830
Now, compare the given values → We know 0.830 ＞0.803, 0.83 is greater.
Problem 3
Solve 2.56 + 0.8
2.56 + 0.8 = 3.36
Explanation
First, we have to align the decimal points:
2.56
+ 0.80
--------
Now, we begin the addition column by column.
Hundredths place: 6 + 0 = 6
Tenths place: 5 + 8 = 13 (write 3, carry 1)
Ones place: 2 + 0 + 1 (carry) = 3
So, we get: 2.56 + 0.8 = 3.36.
Problem 4
Identify the place value of 7 in the number 5.734.
The place value of 7 in 5.734 is tenths or 0.7.
Explanation
The place values are identified from left to right:
5 is in one place.
7 is in tenth place.
3 is in the hundredths place.
4 is in the thousandths place.
Since the digit 7 is in the tenths place, its place value is 7/10 or 0.7.
Problem 5
Round 6.352 to the nearest hundredth.
6.35
Explanation
Here, we identify the hundredths place →5 in 6.352.
Check the digit to the right (thousandths place) → 2.
Since 2 < 5, we round down the value, so the thousandths place remains unchanged.
So, it is rounded to 6.35.
FAQs on Decimal Place Value
1.What do you mean by a decimal place value?
2.What is the significance of decimal values?
3.How can we round a decimal to a specific place value?
4.How do we compare two decimal numbers?
5.How to distinguish a decimal place value from a whole number part value?
6.How can children in United States use numbers in everyday life to understand Decimal Place Value ?
7.What are some fun ways kids in United States can practice Decimal Place Value with numbers?
8.What role do numbers and Decimal Place Value play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Decimal Place Value skills?
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.
