 # How is the Face Value of A Digit Different Than Its Place Value?

It is possible to classify the digits into groups of tens, hundreds, and even thousands of digits using the number system. There is one major difference between the concept of place value and face value. Place value refers to the value of a digit based on its position in a number, while face value refers to the information about the digit (the actual value of the digit).

A number’s face value cannot be altered; however, a number’s place value changes based on the digit’s location.

Let’s explore the definition of both to understand the concept of place value and face value

The concept of place value and face value

Place Value

In any particular number in the number system, each digit has a value called the place value. By multiplying a digit value with its numerical value (ones, tens or hundreds), we can find out the place value of the number.

Example: Let us take the number 78654. To determine the place value of ‘5’, we multiply 5  by 10 and get 50.

The number 5 is placed in tenth place. The place value of the rest of the digits can be found by using the same method.

Face Value

In a number, the face value of each digit is the same as the digit itself.

Example: Let us take a number 98762; 6 itself is the face value of the number 6.

Expanded Form of the Place Value

By considering a number in its expanded form, let’s understand how place value and face value are different and how to find both.

The expanded form of the number 582 is written as 500 80 2.

• The expanded form of a number is given by summing the place values of the digits.
• This example shows that 5 has a place value of 500 (since 5 is in hundreds place), 8 has a place value of 80 (since 8 is in the tens place), and 2 has a place value of 2 (since 2 is in one’s place).
• However, for the same number 582, 5 is the face value of 5, 8 is the face value of 8, and 2 is the face value of 2.

Let us review the expanded form of a number before we proceed to place value and face value.

• The expanded form of the number 534 is written as 500 30 4. Five hundred thirty-four is what we read.
• Similarly, for the number 798, the expanded form = 700 90 8. Seven hundred ninety-eight is what we read.
• Similarly, for 2936 = 2000 900 30 6, we read it as Two thousand nine hundred thirty-six.

As a result, all numbers may be written in expanded form and read accordingly. Readout loud the given number and its expanded form.

(i) 85 = 80 5 = Eighty five

(ii) 732 = 700 30 2 = Seven hundred thirty two

(iii) 972 = 900 70 2 = Nine hundred seventy two

(iv) 4296 = 4000 200 90 6 = Four thousand two hundred ninety six

(v) 3984 = 3000 900 80 4 = Three thousand Nine hundred eighty four

(vi) 2667 = 2000 600 60 7 = Two thousand six hundred sixty seven

The digits of a number express their values when the expanded form and reading of the number are used. A digit’s place value is defined as its value in an expanded form of a number.

In a simple abacus, place face value and value

With the help of an abacus, we will now understand how we can tell the difference between place value and face value. Spike abacus is a tool in which each spike corresponds to a place value, ranging from one to thousands. To understand this, draw an abacus with three spikes, placing ones, tens, and hundred under each spike.

To illustrate, let us look at the number 687-

• Make beads as per the number 687 in each respective spike of the abacus.
• The spikes at the ones position will have 7 beads, then on the spike of tens position draw eight beads, and on the spike of the hundred positions will have 6 beads.
• This means the face value of 7 is 7, and the place value of 7 is 7 x 1 = 5.
• Similarly, the face value of 8 is 8, and the place value of 8 is 8 x 10 = 80, and the same concept applies to the next digit. Find out by yourself and see if you are correct or not.

If you want to make this interesting to learn, colour all the beads using different colours for different spikes.

A comparison of place value and face value

Understanding the differences between place value and face value is essential. Numbers begin with 0 and go up to 10s, hundreds, thousands, and so on in the place value. Check out the following table to learn more about the difference between place value and face value: it lists the major differences between place value and its face value.

Hence, these points are some of the most important differences between the face value and place value. To solve and calculate mathematical expressions, it is essential to know the difference between the two. The above table will give you the points and important facts about place value and face value.

Important Facts about Face Value and Place Value

• If the number has 0 as one of its digits, then the place value of 0 in a given number is always 0.
• As well, 0 has a face value of 0.

Conclusion

It is essential to know how a face value is different from its place value. While reading this section for your exam, don’t forget to make notes and revise all the points after completing the topic; this helps increase retention.

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