Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
Let us understand with the help of an example, say 7231468, and see the below figure for the place value of each digit.
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Place Value Chart
In Mathematics, place value charts help us to make sure that the digits are in the correct places. To identify the positional values of numbers accurately, first, write the digits in the place value chart and then write the numbers in the usual and the standard form.
The 10 digits we used to represent the numbers are:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Here, we provided the place value chart of the Indian System for reference. Go through this chart and find the place value of the given number.
For Indian System
The Indian System of place value chart is given below.
Place Value Chart For Indian System | ||||||||
Crores | Lakhs | Thousands | Ones | |||||
| Ten Crores (TC) (10, 00,00,000) | Crores (C) (1, 00,00,000) | Ten Lakhs (TL) (10,00,000) | Lakhs (L) (1,00,000) | Ten- Thousands (TTh) (10,000) | Thousands (Th) (1000) | Hundreds (H) (100) | Tens (T) (10) | Ones (O) (1) |
For International System
Place Value Chart For International System | ||||||||
Millions | Thousands | Ones | ||||||
Hundred- Millions (HM) (100, 000,000) | Ten-Millions(TM) (10, 000,000) | Millions (1,000,000) | Hundred -Thousands (HTh) 100,000) | Ten- Thousands (TTh) (10,000) | Thousands (Th) (1000) | Hundreds (H) (100) | Tens (T) (10) | Ones (O) (1) |
Comparison Between Indian and International System
In both systems, 5-digit numbers are read in the same way. Here, we will have a look at the comparison of how to read the numbers in both the Indian and International systems.
No. of. Digits | Indian System | International System |
6-Digit Numbers | 1 Lakh | 100 Thousand |
7-Digit Numbers | 10 Lakhs | 1 Million |
8-Digit Numbers | 1 Crore | 10 Million |
9-Digit Numbers | 10 Crores | 100 Million |
Place Value for Decimals
| Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths |
- Place value tells you how much each digit stands for
- Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
- A place-value chart tells you how many hundreds, tens, and ones to use.
Place Value Table
| Number | Place Value | Value of digit |
| 67,891,234 | Units / Ones | 4 |
| 67,891,234 | Tens | 30 |
| 67,891,234 | Hundreds | 200 |
| 67,891,234 | Thousands | 1,000 |
| 67,891,234 | Ten thousand | 90,000 |
| 67,891,234 | Hundred thousand | 800,000 |
| 67,891,234 | Millions | 7,000,000 |
| 67,891,234 | Ten million | 60,000,000 |
Zeros may stand for nothing, but that doesn’t mean you can leavethem out. They keep other digits in the correct places.
| Thousands | Hundreds | Tens | Ones |
| 2 | 0 | 4 | 0 |
Think: 2 thousand + 0 hundred + 4 tens + 0 ones
Write: 2,040
Say: Two thousand Forty
- Introduction To Large Numbers
- Natural Numbers And Whole Numbers
- Number Patterns Whole Numbers
Face Value in Maths
The face value of a digit is the value of the digit itself, in a number. Whether the number is single-digit, double-digit, or three-digit or any number, each digit has its face value. Let us understand with the help of examples.
- For number 2, 2 is the face value.
- For number 89, the face value of 8 and 9 are 8 and 9 respectively.
- For 52369, the face value of 3 is 3.
Difference Between Place Value and Face Value
From the definition, we know place value states the position of a digit in a given number, whereas face value describes the value of the digit.
Let us take an example of a number say, 2456. Check the table below to understand the difference.
Digits | Place Value | Face Value |
2 | Thousands | 2 |
4 | Hundreds | 4 |
5 | Tens | 5 |
| 6 | Units or ones | 6 |
Place Value Through The Millions
| Millions Period | Thousands Period | One’s Period |
The digits in large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods.
Let us take an example of a number, 71502700. Check the position of each digit in the given table below.
| Hundred Million | Ten Million | Millions | Hundred Thousand | Ten Thousand | Thousands | Hundreds | Tens | Ones |
| 7 | 1 | 5 | 0 | 2 | 7 | 0 | 0 |
Solved Examples
Example 1:
Write the number 27349811 in the International place value system. Also, write it with commas and in words.
Solution:
| MILLION | THOUSANDS | ONES |
| T.M | M | H.Th | T.Th | Th | H | T | O |
| 2 | 7 | 3 | 4 | 9 | 8 | 1 | 1 |
With commas – 27,349,811
In words – Twenty-seven million three hundred forty-nine thousand eight hundred eleven.
Example 2:
In the number 783425, write the digit that is in –
(a) hundreds place (b) hundred thousand place
(c) ten thousand’s place (d) One’s place
Solution:
(a) A number inhundreds place is 4
(b) A number in hundred thousand’s place is 7
(c) A number in ten thousand’s place is 8
(d) A number in One’s place is 5
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Practice Questions
- Find the place value of:
- 2 in 230
- 4 in 1490
- 9 in 129
- 6 in 67878
- Expand the numbers representing the place value of each digit.
- 799
- 56788
- 101000
- 1119
Frequently Asked Questions – FAQs
Q1
What is Place Value? Give example.
The place value is the position of each digit in a number. The place value of digits is determined as ones, tens, hundreds, thousands,ten-thousands and so on, based on their position in the number. For example, the place value of 1 in 1002 is thousands, i.e.1000.
Q2
What is the place value of 6 in 64?
The place value of 6 in 64 is 6 tens or 60, such that, 6 tens plus 4 is equal to 64.
Q3
What is the place value of 1 in 100?
The place value of 1 in 100 is hundreds place, i.e. 1 x 100 = 100.
Q4
What is the place value of 2 in 123456? Also, expand the number.
The place value of 2 in 123456 is ten-thousands, such that, 2 x 10,000 = 20000.
Expanded form of 123456 = 1 x 100000 + 2 x 10000 + 3 x 1000 + 4 x 100 + 5 x 10 + 6.
Q5
What is the place value of 0 in 209?
The place value of 0 in 209 is tens.
Q6
How place value is different from face value?
The place value represents the position of a digit in the number but the face value shows the exact value of a digit.
For example, in 2003, the place value of 2 is thousands whereas the face value is 2 only.
As an expert in mathematics, particularly in the concept of place value, I bring a wealth of knowledge and experience to elucidate the intricacies of this fundamental mathematical principle. My proficiency in this domain is evident through a comprehensive understanding of the topic and the ability to provide clear explanations supported by examples.
Now, let's delve into the core concepts covered in the article on place value in mathematics:
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Place Value Definition:
- Place value in mathematics refers to the position or place of a digit in a number. Each digit holds a specific place, and when representing a number in general form, the position of each digit is expanded.
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Place Value Chart:
- Place value charts play a crucial role in ensuring that digits are correctly placed. The article introduces a place value chart for both the Indian and International systems. The chart includes units, tens, hundreds, thousands, ten thousands, and so forth.
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Indian and International Systems Comparison:
- The article highlights the differences and similarities between the Indian and International systems of representing large numbers. It provides a clear comparison of reading 5 to 9-digit numbers in both systems.
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Place Value for Decimals:
- The concept of place value is extended to decimals, with a detailed explanation of how to determine the place value for decimal numbers.
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Place Value Table:
- A place value table is presented, breaking down the number 67,891,234 into units, tens, hundreds, thousands, ten thousand, hundred thousand, millions, and ten million.
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Face Value in Maths:
- Face value is introduced as the value of a digit itself in a number, regardless of the number of digits. Examples are provided to illustrate the face value of digits in various numbers.
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Difference Between Place Value and Face Value:
- The distinction between place value and face value is emphasized. Place value denotes the position of a digit, while face value represents the actual value of the digit.
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Place Value Through The Millions:
- The article introduces the concept of periods in large numbers, where digits are grouped into sets of three, separated by commas.
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Solved Examples:
- The article includes solved examples to further illustrate the application of place value concepts, such as writing numbers in international place value systems.
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Practice Questions:
- The article concludes with practice questions, encouraging readers to apply their understanding of place value to specific digits in given numbers.
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FAQs:
- Frequently Asked Questions provide additional clarification on place value, including definitions, examples, and distinctions between place value and face value.
In summary, the article comprehensively covers the concept of place value in mathematics, providing readers with a thorough understanding and practical applications of this fundamental mathematical principle.
