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Difference Between Place Value And Face Value, Examples, Important Topics

Difference Between Place Value And Face Value : Read everything you need to know about the numbers. Learn about the difference between place value and face value of a number.

Shrivastav 16 Jan, 2024

Difference Between Place Value And Face Value : Place value and face value are essential concepts in mathematics, especially in the area of number theory. Understanding the numerical value of digits in numbers, particularly in large and complex numbers, requires an understanding of these principles.

We will discuss the difference between place value and face value as well as their significance for mathematics understanding and computations. People frequently mix up the two terms and use them interchangeably, misunderstanding their true meaning. However, we need to be aware that there is a big difference between place value and face value. A number's Place value refers to where it falls inside that specific number, but a digit's Face value represents its real value.

Before we discuss the difference between place value and face value, let’s first learn the definitions of place value and face value. Achieve JEE excellence with PW JEE Online Course . Join now to fulfill your engineering dreams!

Definition of Place Value

Definition of Place Value : The Indian numbering system's base is widened by place value or positional notation. More broadly speaking, the value of a digit in a number is its multiplicity by its position in the number, and this is known as a place value or positional notation. Early in the 14th century, the idea of place value was developed. Before then, a digit could only have one value—face value in early Roman and number systems—according to conventional thought.

Positional notation originated with the Babylonian mathematicians. It was quite difficult to compute at the time since base 60 was in use. With the introduction of the decimal numbering system in modern times, which is based on base 10, place value calculations are made very simple.

The concept of place value helps us understand how numbers function dependent on the positions of their digits. A number's values are assigned to each digit based on where it lies in the number; the value of the rightmost digit is 1, and the values of the subsequent digits to the left increase by 10 times.

Take the number 456 as an example. The place value of the number 6 is only 6 since it is in the "ones" place. Due to its placement in the "tens" position, the value of the digit 5 is 50 (5 times 10). 400 (4 times 100) is the place value of the digit 4, which is in the "hundreds" place.

Definition of Face Value

Definition of Face Value : The Face value, also referred to as the "nominal value," is just a number's true worth. It cannot be changed by the place shift of a digit in a number, as compared to the place value. Let's try to determine the face value of the two identical digits in the number 7780. In this case, both sevens will have the different place values, which are 7000 for the first seven and 700 for the second.

It is observed that students often struggle to understand the concept. Thus, we came up with a method for helping you retain the concept. Place value may be considered as the value of a digit with respect to its position, while face value is the value of a coin, person, or other object that remains constant regardless of the situation. Similar to this, a number's face value is fixed and equal to the number itself.

Key Difference Between Place Value and Face Value

Key Difference Between Place Value and Face Value : It is important to understand the basic distinctions between face value and place value. The number system extends to tens, hundreds, thousands, and so on, starting at zero. See the table below for a more thorough explanation of the important difference between place value and face value:

Difference Between Place Value and Face Value
Basis of Comparison	Place Value	Face Value
Definition	The value of a digit based on its position in a number	The value of a digit in isolation
Calculation	Calculated by multiplying the digit with its positional value (power of 10)	Simply the digit itself
Position	Depends on its position in a number	Remains the same regardless of its position in a number
Significance	Important in determining the overall value of a number	Important in identifying individual digits in a number
Example	In the number 54321, the place value of 4 is 40,000	In the number 54321, the face value of 4 is 4

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Place Value and Face Value Examples

Place Value and Face Value Example : Let's understand the concepts through the number's expanded form. Now, let's discuss 2768 in this example. Expanded form for 2768. 2768= 2000+700+60+8 A number's expanded form gives the total of the place values for all of its digits. For 2 the place value is 2000, 700 for 7, 60 for 6, and 8 for 8. However, when it comes to face values, the numbers are just as valued as the numbers themselves. Similar to the situation above, 2 has a face value of 2, 7 has a face value of 7, 6 has a face value of 6, and 8 has a face value of 8 as the only number.

Difference Between Place Value and Face Value FAQs

Q1: What is a number's place value? Could you give an example?

Ans. The place value of a digit determines its position inside a number. One unit, tens of units, hundreds of units, and so on. For example: 6 x 100 = 600 is the hundredth-place value of 6 in 59648.

Q2: What are the place value and face value of 2 and 7 in 259784?

Ans. Place values: 7 is 700 and 2 is 200000. Face Values: 2 is 2, 7 is 7.

Q3: Does Face Value depend on where a digit appears in a number?

Ans. A digit’s face value does not depend on the position it is appearing in a number.

Q4: What is the face value of 4 in 5432?

Ans. The face value of 4 in the number 5432 is 4.

Q5: What is the place value and face value of 2 in 829?

Ans. The place value of 2 is in the tenth position in the number 829. As a result, 2 has a place value of 20 and a face value of 2.

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Definition of Place Value

Definition of Face Value

Key Difference Between Place Value and Face Value

Difference Between Place Value and Face Value
Basis of Comparison	Place Value	Face Value
Definition	The value of a digit based on its position in a number	The value of a digit in isolation
Calculation	Calculated by multiplying the digit with its positional value (power of 10)	Simply the digit itself
Position	Depends on its position in a number	Remains the same regardless of its position in a number
Significance	Important in determining the overall value of a number	Important in identifying individual digits in a number
Example	In the number 54321, the place value of 4 is 40,000	In the number 54321, the face value of 4 is 4

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