The face value of the number is described as the value of the digit itself. The place value is defined as the position of the digit in the number. The basic difference between the place value and the face value is that the place value tells the value of a digit based on its position in a number, whereas the face value is the actual value of the digit in the number. 

The face value of the number is definite, and it cannot be changed, whereas the place value of the number changes according to the digit’s place. The number system is important for characterising the digits in ones, tens, hundreds, thousands, etc. In this article, we will provide detailed information on place and face value. Scroll down to learn more!

Definition of Face and Place Value

Face value: The face value of the number can be shown as the value of the digit itself. For example, the face value of the digit \(7\) in the number \(8976\) is \(7\) itself.
Place value: The place value shows the position of the digit in the number. For example, the place value of the digit \(6\) in \(9863\) is tens as \(6 \times 10 = 60\)

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Place Value of a Number

You have already seen that a \(4\) digit number contains the following place value:

1. Thousands
2. Hundreds
3. Tens and
4. Units

That is why the multiplier to be utilised for each of the digits of a \(4\)-digit number is \(1000,100,10,\) and \(1.\)
Now, try and examine the given number, \(2365.\)
\(2365 = \left({2 \times 1000}\right) + \)
\(\left({3 \times 100} \right) + \)
\(\left({6 \times 10}\right) + \)
\(\left({5 \times 1} \right)\)
\( = 2000 + 300 + 60 + 5 = 2365\)
Now, you can consider the given numbers \(2365,2635,2563,\) and \(3652.\)
And you might have noticed the value of the same digit \(3\) in each of these numbers.
\(2365 \to 3\) has hundreds place and a place value of \(300.\)
\(2635 \to 3\) has tens place and a place value of \(30.\)
\(2563 \to 3\) has units place and a place value of \(3.\)
\(3652 \to 3\) has thousands place and a place value of \(3000.\)
This tells us that the value of a digit is not the only thing that determines its place value in a \(4\)-digit number.

Face Value of a Number

The face value of a digit in a number is the same digit itself. For instance, in the number 548, the face value of 4 is 4, whereas, in the place value system the value is tens i.e. 40. The face value does not depend on the position or the place of the digit in the number. Let us consider some examples for better clarity of Face Value of a Number:

Try and examine the given number, \(98578.\)

The face value of the digit 9 in the number \(98578\) is \(9\)
The face value of the digit 8 in the number \(98578\) is \(8\)
The face value of the digit 5 in the number \(98578\) is \(5\)
The face value of the digit 7 in the number \(98578\) is \(7\)
The face value of the digit 8 in the number \(98578\) is \(8.\)

Difference Between Place Value and Face Value

The main difference between the place value and the face value is that the place value tells us the digit’s position, whereas the face value represents the actual value of the digit. The number system is available and is vital for characterising the digits in ones, tens, hundreds, thousands, etc. The difference between the place value and the face value is given below:

Place value	Face value
The place value represents the position or the place of digit in the number.	The face value of the digit represents the value of the digit itself.
Each digit of the number has a value that depends on its place.	The face value does not depend on the position or the place of the digit in the number.
\({\text{Place}}\,{\text{value}}\,{\text{of}}\,{\text{digit}} = {\text{face}}\,{\text{value}} \times {\text{numerical}}\,{\text{value}}\,{\text{of}}\,{\text{place}}\)	\({\text{Face}}\,{\text{value}}\,{\text{of}}\,{\text{the}}\,{\text{digit}} = {\text{numerical}}\,{\text{value}}\,{\text{of}}\,{\text{the}}\,{\text{digit}}\,{\text{itself}}\)
The place value of the number zero will always be zero only.	The face value of zero is zero only.
Example: place value of \(9\) in the number \(89765\) is \(9 \times 1000 = 9000\)	Example: The face value of the digit \(9\) in the number \(89765\) is \(9 = 9.\)

Place and Face Value Chart

While reading the numbers, it is always easy to use the words instead of reading individual digits. For example: Instead of reading \(527\) as Five, two, seven, it is easy to read as Five hundred and twenty-seven.

There are a couple of commonly used methods of numeration, and they are as follows:

1. The Indian system of numeration
2. The International system of numeration

What is the Indian System of Numeration?

The Indian numeration system is based on the Vedic numbering system. In this, you have to split up the given numbers into groups or in periods. You have to start from the extreme right digit of the given number and move on to the left. The first three digits are on the extreme right for a group of ones. The digits in one column are in turn and split into hundreds, tens and units.

The second group of the next two digits on the left of the group of ones form the group of thousands, further split into thousands and ten thousand. The third group of the following two digits on the left of the group of the thousands build the group of the lakhs divided into lakhs and ten lakhs. Then the two digits on the left side of the group of lakhs build a group of crores divided into crores and ten crores.

Indian Place Value Chart

In the Indian system of numeration, each digit of the number has a place value and face value. The place value of the digit depends on the digit’s position, whereas the face value does not depend on the position of the digit.

Example: In the number name “Six thousand eight hundred forty-seven,” that is the number \(6847,\) the face value of \(7\) is \(7.\) In the same way, the face value of the numbers \(4,8,\) and \(6\) are also \(4,8,\) and \(6,\) respectively. You can see the digits given below:
The number \(7\) has the place value \(7 \times 1 = 7,\) since it is in the unit’s place.
The number \(4\) has the place value \(4 \times 10 = 40,\) since it is in the tens place.
The number \(8\) has the place value \(8 \times 100 = 800,\) since it is in the hundreds place.
The number \(6\) has the place value \(6 \times 1000 = 6000,\) since it is in the thousands place.
It is evident from this that the number is the sum of the place values of all the digits of the number.
Also, the formula is as given: Place value of a digit \( = \) Face value \( \times \) Position value.

What is the International System of Numeration?

The International System of numeration is followed by most of the countries in the world. In this system, the number is divided into groups or in periods. You need to start from the extreme right digit of the number to build the groups. The groups are known as the ones, thousands, millions, and billions.

The digits in one column are in turn and split into the hundreds, tens, and units. Then the second of the next three digits on the left side of the group of the ones build the group of the thousands, which is further divided up into the thousands, ten thousand, and the hundred thousand. Then the third group of the next three digits on the left side of the group of the thousands form the group of the millions. Three digits on the left side of the group of the millions form the group of the billions which is divided into billions, ten billion, and the hundred billion. It is shown below in the tabular form:

International System of Numeration Chart

Below we have provided the international system of numeration chart for your reference:

Solved Examples on Place and Face Value

Q.1. Find the difference of the place values of two 8’s in the number 578493087.
Ans: By inserting commas to separate periods, the given number can be written as:

So, the number is \(57,84,93,087\)
We observe that the \(8\) in the second place from right is at ten’s place.
So, place value of \(8\) in ten’s place \( = 8 \times 10 = 80\)
The second \(8\) is at the ten lakh’s place.
So, place value of \(8\) in ten lakh’s place \( = 8 \times 1000000 = 8000000\)
Hence, the required difference \( = 8000000 – 80 = 7999920.\)

Q.2. Write the expanded form of the numbers 8976 and 3482.
Ans: Given, the numbers \(8976\) and \(3482\)
You need to write the expanded form of the given two numbers.
So, in \(8976,\) you can see that the digit \(8\) is in the thousands, \(9\) is in the hundreds, \(7\) is in the tens, and \(6\) is in the ones.
Now, \(8976 = 8000 + 900 + 70 + 6\)
In the same way, in \(3482,\) the number \(3\) is in the thousands place, \(4\) is in the hundreds place, \(8\) is in the tens place, and \(2\) is in the one’s place.
Thus, \(3482 = 3000 + 400 + 80 + 2\)
Hence, the expanded form of \(8976\) is \(8000 + 900 + 70 + 6\) and \(3482\) is \(3000 + 400 + 80 + 2.\)

Q.3. Identify the place value and compare the given numbers 6789 and 6743.
Ans: Given the numbers to compare are \(6789\) and \(6743\)
When you want to compare any number, we start comparing from the left side from thousands places.
So, we can see that the digits in the thousands place and the hundreds place are the same.
Now, compare the tens place digits \( \to 8 > 4.\)
Here, you can clearly see that the number \(8\) is greater than the number \(4.\)
This means \(6789\) is the greater number than the number \(6743.\)
Hence, the required answer is \(6789 > 6743.\)

Q.4. Write the place value of a digit 7 in the number 26798.
Ans: We have, the number is \(26798\)
So, we will write the number in the place value table.

Ten thousand	Thousands	Hundreds	Tens	Ones
\(2\)	\(6\)	\(7\)	\(9\)	\(8\)

Now, you can see the digit \(7\) is in the hundreds place, which means \(7 \times 100 = 700\)
Hence, the place value of digit \(7\) is \(700.\)

Q.5. Write the place value of a digit 9 in the number 98708.
Ans: We have, the number is \(26798\)
So, we will write the number in the place value table.

Ten thousand	Thousand	Hundreds	Tens	Ones
\(9\)	\(8\)	\(7\)	\(0\)	\(8\)

Now, you can see the digit \(9\) is in ten thousands place, which means \(9 \times 10000 = 90000\)
Hence, the place value of the digit \(9\) is \(90000.\)

Summary

The place value of a number is defined as the position or the place of a digit in the number. The face value of any number can be represented as the value of the digit itself. The place and face value can be calculated by using various methods like the Indian system of numeration and the International system of numeration.

In the International system of numeration, the number is divided into groups or in periods. In the Indian system of numeration, every digit of the number has a face and place value. The place value of the digit relies on the digit’s position. The face of the digit does not rely on the position of the digit.

FAQs on Place and Face Value

Q.1. What are place value and face value in mathematics?
Ans: Place value tells us the position of the digit in the number and face value of any number that can be shown as the value of the digit itself.

Q.2. What is the place and the place value in maths?
Ans: In mathematics, every digit has a place, and the place value can be defined as the value represented by the digit to tell its position in any number.

Q.3. Write the face value of digit 2 in the number 624.
Ans: The face value of the digit \(2\) in the number \(624\) is the number itself, and that is \(2.\)

Q.4. What is the place value of 3 in 23?
Ans: The place value of the digit \(3\) in the number \(23\) is \(3\) as it is in the ones place, so \(3 \times 1 = 3.\)

Q.5. Explain the face value of a digit with an example.
Ans: The face value of a digit in a number is the same digit itself. For instance, consider the number \(738.\) The face value of the digit \(8\) in the number \(738\) is \(8.\)

Q.6. What is the difference between the place and the face value of a number?
Ans: The place value is defined as the position or the place of a digit in the number. On the other side, the face value is described as the face value of a digit in a number is the same digit itself.

We hope this detailed article on place and face value helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!