Place Value
Place value, in mathematics, describes the value of every digit in a number depending on its position. These positions start from the units place (ones place). The order of the place value of digits in a number from right to left is expressed as ones/units, tens, hundreds, thousands, ten thousands, and so on. Let us learn more about the place value meaning, some place value examples along with the place value table.
| 1. | What is Place Value? |
| 2. | Place Value Chart |
| 3. | Place Value Chart with Decimals |
| 4. | Place Value and Face Value |
| 5. | FAQs on Place Value |
What is Place Value?
Place value is the value of each digit in a number. The value of every digit in a number is different based on its position. A number might have two similar digits but different values, which is decided by the position that the digit holds in the number.
Place Value Definition
Place value is the value of a digit according to its position in the number such as ones, tens, hundreds, and so on. For example, the place value of 5 in 3458 is 5 tens, or 50. However, the place value of 5 in 5781 is expressed as 5 thousands or 5,000. It is important to understand that a digit can be the same, but its value depends on its position in the number.
Example: Write down the place value of each digit in the number 543.
Solution: The correct place value of each digit in the number can be expressed as follows:
- 5 × 100 = 500 or 5 hundreds
- 4 × 10 = 40 or 4 tens
- 3 × 1 = 3 or 3 ones
Place Value Chart
Number Place value charts help us to make sure that the digits are aligned in the correct places. A number place value chart displays the correct position or place of a digit in a number. To identify the positional values or worth of different digits in a number accurately, we first write the given digits in the number place value chart to check their position. In order to make the process easier, the larger numbers are divided into periods that are separated with the help of commas. There are two types of place value charts that are most commonly used:
- Indian place value chart
- International place value chart
We can refer to the International or Indian place value chart based on the numeral system that both the charts follow. The Indian place value chart is based on the Indian numeral system, while the International place value chart is based on the Internationally accepted numeral system. The main difference between the Indian and the International numeral system is the placement of the separators (commas) and the nomenclature of different place values.
Indian Place Value Chart
The Indian place value chart is a table that is used to find the value of each digit in a number based on its position, as per the Indian numeral system. In this place value chart, a 10-digit number is grouped into periods of ones, thousands, lakhs, crores, and so on. These numbers are separated by commas following the rule of 3:2:2. This means starting from the right, the first comma is placed after 3 digits, then the next commas are placed after every 2 digits. For example, observe the commas in the following number: 5,43,13,62,283
Observe the Indian place value chart given below which shows the place value of digits till ten crores.
International Place Value Chart
The International numeral system is used worldwide in which we count in the order of ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, and so on. In this place value chart, the numbers are grouped into periods of ones, thousands, millions, and so on and they are separated by a comma after every 3 digits, starting from the right. For example, observe the commas in the following number: 135,912,332. Observe the International place value chart given below which shows the place value of digits up to hundred millions.
Printable Place Value Charts
Memorizing and solving problems on place value systems becomes easier using a printable number place value chart. These charts have place values printed in a tabular form across blank spaces for each digit in a number. While referring to these charts for solving a problem, we can directly place the digits in their respective position according to the one in the number and evaluate their place values accordingly.
Place Value Chart with Decimals
The decimal place value chart shows the place value of the digits in a decimal number. A decimal number system is used to express the whole numbers and fractions together using a decimal point. This decimal point lies between the whole number part and the fractional part. While the whole number part follows the usual place value chart of ones, tens, hundreds, and so on, there is a slight difference in the place value of the numbers to the right of the decimal point. If we go to the right after the decimal, the place values start from tenths and go on as hundredths, thousandths, and so on. The first place to the right of the decimal is on the one-tenth (1/10th) position, the next one is 1/100 and it goes on. Observe the following place value chart for decimal numbers.
Place Value and Face Value
The face value of a digit in any number is the digit itself. Whether the number is single-digit, double-digit, or any number, each digit has its face value. Let us understand this using the following examples.
- If 4 is the given number, the face value of 4 is 4, and the place value of 4 is also 4 (4 ones = 4 × 1 = 4).
- For a given number 78, the face value of 7 is 7 and its place value is 70 (7 tens = 7 × 10 = 70).
- For 52369, the face value of 3 is 3 while its place value is 300 (3 hundreds = 3 × 100 = 300).
Difference between Place Value and Face Value
Place value describes the position of a digit in a given number. On the other hand, face value represents the number itself. Let us take an example of a number say, 1437. The table given below explains the difference between the place value and the face value of digits in this number.
|
Digits in the number 1437 |
Place Value | Face Value |
|---|---|---|
|
1 |
1 Thousand (1 × 1000 = 1000) |
1 |
|
4 |
4 Hundreds (4 × 100 = 400) |
4 |
|
3 |
3 Tens (3 × 10 = 30) |
3 |
| 7 | 7 Units or ones ( 7 × 1 = 7) |
7 |
Place Value in Numbers
The place value in numbers can be expressed in two different ways. For example, the place value of 4 in 2458 can be expressed as 4 hundreds, or 400. In another example, the place value of 4 in 4681 is expressed as 4 thousands or 4,000.
In simple terms, if we need to express the place value in the number form we simply multiply the number with the name of the column under which it falls. For example, if we need to find the place value of 5 in 67538, we will first place the given number under the place value chart such that each digit is placed correctly under the respective column. In this case, we can see that 5 comes under the hundreds column. So, we can say that the place value of 5 is 5 × 100 = 500. Therefore, the place value of 5 is 500 in the given number.
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FAQs on Place Value
What is Place Value in Math?
Place value is the value of each digit in a number. The value of every digit in a number is different based on its position. A number might have two similar digits but different values, which is decided by the position that the digit holds in the number. For example, the place value of '9' in the number 8934 is 9 hundreds or 900 because 9 is on the hundreds place.
How to Find the Place Value of a Number?
In order to find the place value of a number, we need to know that the value of every digit in a number is different based upon its position. A large number might have two similar digits but different values, which is decided by the position that the digit holds in the number. For example, the place value of 6 in 3468 is 6 tens, or 60. However, the place value of 6 in 6781 is expressed as 6 thousands or 6,000. It is important to understand that a digit can be the same, but its value depends on its position in the number.
What is the Place Value of 6 in 64?
Since 6 is in the tens place, the place value of 6 in 64 is 6 tens, i.e., 6 × 10 = 60.
What is an Example of Place Value in Numbers?
Place value represents the worth of a digit in a number. A few examples of place values are given below:
- The place value of 2 in 24 is 2 × 10 = 20.
-
The correct place value of each digit in the number 543 can be given as follows: The place value of 5 is 5 × 100 = 500; the place value of 4 is 4 × 10 = 40; the place value of 3 is 3 × 1 = 3
What is the Place Value of 5 in 50?
Place value is the value of each digit in a number. The place value of the digit 5 in 50 is 5 tens, i.e., 5 × 10 = 50.
What is Place Value and Face Value with Example?
The face value of a digit in any number is the digit itself, while its place value is its position in the number. For example, the face value of 7 in 2769 is 7 while its place value is 7 hundreds or 700.
What is a Place Value Chart?
A place value chart is a table that is used to find the value of each digit in a number based on its position, as per the numeral system. In order to identify the worth of different digits in a number accurately, we place the given number in the place value chart so that the place value of each digit is seen. To make the process easier, the larger numbers are divided into periods that are separated with the help of commas. There are two types of place value charts that are most commonly used, the Indian place value chart and the International place value chart.
How to Make a Place Value Chart?
To make a place value chart, we can use the following steps:
- Step 1: Draw columns showing different periods according to the type of numeral system: ones, tens, hundreds, thousands, and so on.
- Step 2: Under each period, draw sub-columns to show the different place values.
You can refer to the Indian place value chart and International place value chart in the above sections for the different periods and place values of a digit in a number according to the type of numeral system.
Why is Place Value in Numbers Important?
The concept of place value in numbers is important because it gives the worth of every digit in a number according to its position. The essence of numbers as a whole can only be understood through the knowledge of place values.
What is the Place Value of Zero?
The place value of zero is always zero. For example, in a given number 4078, zero comes under hundreds place. So, this is expressed as, 0 hundreds, that is, 0 × 100 = 0.
How to Find the Place Value in Decimal Numbers?
In decimal numbers, the place value of the digits after the decimal is expressed in a little different way. We know that a decimal number consists of a whole number and a fractional part which is written after the decimal point. The whole number part follows the usual place value chart of ones, tens, hundreds. Now, if we go to the right after the decimal, the place values start from tenths and go on as hundredths, thousandths, and so on. For example, let us write the place value of all the digits in the following decimal number: 578.43
- 5 comes under the hundreds column, therefore, the place value of 5 is 5 hundreds, or 5 × 100 = 500
- 7 comes under the tens column, therefore, the place value of 7 is 7 tens, or 7 × 10 = 70
- 8 comes under the ones column, therefore, the place value of 8 is 8 ones, or 8 × 1 = 8
- 4 comes under the tenths column, therefore, the place value of 4 is 4 tenths, or 4/10 = 0.4
- 3 comes under the hundredths column, therefore, the place value of 3 is 3 hundredths, or 3/100 = 0.03