Difference Between Place Value and Face Value

Place value and face value are two different mathematical terms that are often confused, but they are fundamental concepts in number systems. Let us explore the difference between them using an example.

Consider the number 325.

• The face value of the digit 2 in this number is simply 2.
• The place value of the digit 2 in this number depends on its position. The digit 2 is in the tens place, meaning its place value is two times 10 or 20.

Similarly, for the digit 5:

• The face value of the digit 5 in this number is simply 5.
• The place value of the digit 5 in this number is five times 100, or 500, because it is in the hundreds place.

Finally, for the digit 3:

• The face value of the digit 3 in this number is simply 3.
• The place value of the digit 3 in this number is three times 1, or 3 because it is in the one's place.

In any numbering system, the position of a digit in a number determines its place value. For example, in the decimal system (the most commonly used numbering system), the first position to the right of the decimal point represents the tenth place, the second position represents the hundredth place, and so on. Similarly, to the left of the decimal point, the first position represents the one's place, the second position represents the tens place, the third position represents the hundreds place, and so on.

On the other hand, the face value of a digit is simply the value of the digit itself, regardless of its position in the number. For example, in the decimal system, the face value of the digit "3" in the number 352.1 is simply 3, regardless of whether it is in the ones place, the tens place, or the hundreds place.

Understanding the numbering system is crucial for determining the place value and face value of digits in a number. By understanding the position of each digit in the number and its corresponding place value, we can determine the overall value of the number. By understanding the value of each digit, we can determine the overall face value of the number.

What is Place value?

Place value or positional notation expands any base of the Indian numbering system. In a more generalized way, a place value or positional notation is the value of the digit in the number, which is determined by the digit multiplied by the place of the digit in the number. The concept of place value came in the early 14th century. Before that, it was considered in roman and early numeral systems that a digit could have only one value, which was face value at that time.

The Babylonian mathematicians first developed the concept of positional notation. At that time, base 60 was used, and it was very complex to calculate.

In the modern era, we have the Decimal system of numbering, which is based on base 10, which is very easy in the case of calculation and place value calculation.

Place value is a way of understanding how numbers work based on the position of their digits. Each digit in a number has a value determined by its position within the number, with the rightmost digit having a value of 1 and each successive digit to the left has a value ten times greater than the previous digit.

For example, let us take the number 456. The digit 6 is in the "ones" place, meaning its place value is simply 6. The digit 5 is in the "tens" place, so its place value is 50 (5 times 10). The digit 4 is in the "hundreds" place, so its place value is 400 (4 times 100).

Understanding place value is an essential concept in mathematics. It is used in many mathematical operations like addition, subtraction, multiplication, and division. By learning about place value, students can build a strong foundation in math that helps them as they advance to more complex topics.

Place value is also relevant beyond the classroom. It is used in computer science to represent and manipulate numbers in binary and other number systems. In these contexts, the value of a digit is determined by its position relative to the base of the number system being used.

In the number 67,329, the place values of:

• Six is in the ten thousand places and has a place value of 60,000.
• Seven is in the thousand's place and has a place value of 7,000.
• Three is in the hundreds and has a place value of 300.
• Two is in the tens place and has a place value of 20.
• Nine is in the one's place and has a place value of 9.

What is Face Value?

The Face value, also known as "nominal value," is only the actual value of a number. Unlike the place value, it is not changeable with the place change of a digit in a number. So, let us try to find the face value of two same digits in the number 7780; here, both seven will have the same face value as seven, and when it comes to their place value, they are 7000 and 700 for the first and second 7, respectively.

A common intuition comes into our minds on remembering face value and place value concepts. It is seen that students usually get confused with the concept.

So, we have come forward with a trick for remembering the concept. You can consider the place value as the value of a digit with its place, and for face value, just the face of a person, a coin, etc., does not change even in any circumstance. Similarly, the face value of a number is unchangeable, and its value is the number itself.

Some facts about Face Value.

• It is the actual value of a digit in a number
• It does not change for a particular digit in a number even after the change in place or number.
• The face value does not change for a digit; let us say 7 in 6789 and 9967; the face value of 7 in both numbers is the same.
• It is the value of the digit itself.
• Face value is different from place value.

Difference Table