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Updated on 26th April, 2024 , 8 min read
In the realm of mathematics, particularly in the study of numbers and their properties, two fundamental concepts play significant roles: place value and face value. While these terms may seem similar at first glance, they hold distinct meanings and serve different purposes in numerical representation. In this comprehensive exploration, we will delve into the definitions, significance, and applications of place value and face value, elucidating their differences and illustrating their importance in mathematical operations and problem-solving. The primary distinction between place value and face value is that the place value deals with the digit's location, whereas the face value indicates the real value of a digit. The number system is provided and is required for classifying digits into groupings of tens, hundreds, and thousands.
With the use of an enlarged form of a number, the notion of face value and place value of a digit may be better understood.
For Example: 842 = 800 + 40 + 2
= 8 × 100 + 4 × 10 + 2 × 1
The following table shows the enlargement of place and face value-
Digits | Place Value | Face Value |
8 | 800 | 8 |
4 | 40 | 4 |
2 | 2 | 2 |
The above table provides the solution to the question: What is the face value and place value of a digit in a number?
Any number's face value can be expressed as the value of the digit itself. Place value refers to the value of each digit in a number. We calculate a number's place value by multiplying its digit value by its numerical value. Face value, on the other hand, refers to the inherent numerical value of a digit itself, irrespective of its position within a number. Unlike place value, which depends on the position of a digit within a numeral, face value represents the actual numerical quantity represented by the digit itself. In essence, the face value of a digit is the value it carries on its own, independent of its placement within a number.
For example, in the number 3,457.29:
In this context, face value simply denotes the numerical quantity represented by each digit, without consideration for its position within the numeral.
For Example: Find the face value of each digit in the number 4856.
Solution: Every digit's face value is the number itself.
The face value of '4' is four.
The face value of '8' is eight.
The face value of the number '5' is five.
The face value of the number '6' is six.
Place value is a foundational concept in mathematics that forms the basis for understanding numerical operations, place notation, and arithmetic algorithms. It enables efficient numerical representation and manipulation by organizing digits into meaningful positions that reflect their relative magnitudes. By assigning specific values to digits based on their positions within a number, place value facilitates addition, subtraction, multiplication, division, and other mathematical operations with ease and precision. Furthermore, place value plays a crucial role in extending the decimal number system to represent numbers of varying magnitudes, both large and small. Through the use of place notation and exponential notation, place value allows for the concise expression of numbers spanning multiple orders of magnitude, making it indispensable in scientific notation, engineering, finance, and other fields where large or small quantities are encountered.
For example, in the number 3,457.29:
In essence, place value assigns a numerical value to each digit in a number based on its position, facilitating accurate numerical representation and computation.
The position of a digit in a number is represented by its place value. Determine the place value of each digit in the integer 4856. To determine the place value of the numbers in the number 4856, multiply each number by the digit value.
The distinction between place value and face value is made using the extended form of a number. 5689 in its enlarged form equals 5000 + 600 + 80 + 9. In the extended form, we express a number as the sum of the place values of each digit. The place value of 5 in the number 5689 is 5000 (since 5 is in the thousands place), the place value of 600 (since 6 is in the hundreds place), the place value of 8 is 80, and the place value of 9 is 9. (since 9 is in ones place). However, the face value of 5 in the same number 5689 is 5, the face value of 6 is 6, the face value of 8 is 8, and the face value of 9 is 9.
The following are the properties of place value-
The number system in place means values range from 0 to tens, hundreds, thousands, and so on. The following table gives more information about the key distinctions between place value and face value-
Place Value | Face Value |
The place value describes the position or place of a digit in a given number. | The digit itself within a number is simply defined as having a face value. |
For Example- The place value of 5 in the number 452 is (5 10) = 50 because 5 is in the tens place. | For Example- The face value of 6 in the number 360 is 6. |
Place Value = Face Value x numerical value of place. | Face value of digit = numerical value of the digit itself. |
The place value of 0 is 0. | The place value of 0 is 0. |
To get a number's place value, multiply its digit value by its numerical value. | The face value of a digit is always the same, regardless of where it is positioned. |
The value indicated by a digit in a number based on its position in the number is known as place value. | The face value of a digit in a number is its real value and is independent. |
Understanding the distinctions between place value and face value is essential for various mathematical applications and problem-solving scenarios. Some examples of their applications include:
When reading numbers, it is usually easier to use words than individual digits. For example, instead of reading 527 as 5, 2, 7, it is simple to read 527 as five hundred and twenty-seven. There are two frequently used numeration methods, which are as follows-
The Vedic numbering system is the foundation of the Indian numeration system. For this one must divide the provided integers into groups or periods. Students must begin with the extreme right digit of the supplied number and work their way to the left.
The International System of Numbers is used by the majority of the world's countries. The total is split into groups or periods in this approach. To form the groups, one must begin with the number's extreme right digit. The various groups are referred to as the ones, thousands, millions, and billions. The digits in one column are divided into hundreds, tens, and units. The following three numbers on the left side of the group of ones form the group of thousands, that is further subdivided into thousands, ten thousand, and a hundred thousand. The group of millions is formed by the third group of the following three numbers on the left side of the group of thousands. Three numbers on the left side of the million groups create the billion group, which is split into billions, ten billion, and hundred billion.
Example 1: Find the Place and Face values for each digit in the number 4657.
The following table shows the place value and face value of the digits-
Digits | Place Value | Face Value |
6 | 6000 | 6 |
2 | 200 | 2 |
3 | 30 | 3 |
4 | 4 | 4 |
As a result, these are some of the fundamental distinctions between face value and place value. It is critical to understand the differences between the two because they are both utilized in mathematical expressions to solve and compute.
A number's place value is defined as the position or location of a digit inside the number. Any number's face value can be expressed as the value of the digit itself. Various systems, such as the Indian system of numeration and the International system of numeration, can be used to compute the place and face value. The numbers are split into groups or periods in the International method of enumeration. Every digit of a number has a face and a place value in the Indian system of numeration. The digit's place value is determined by its location. The location of the digit has no bearing on the face of the digit.
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By - Nikita Parmar 2024-09-06 10:59:22 , 6 min readAns. The face value of a digit in a number determines the number’s value. It makes no difference what position the digit is in. For example, the face value of 9 in 911 is simply 9.
Ans. 2 in 93207 has a face value of 2.
Ans. A digit’s place value in a number determines where it is put or positioned. It may be in the first place, the tenth place, the hundredth position, and so on. For example, the place value of 5 in 252 is 5 x 10 = 50, which is the tenth place.
Ans. The place value of 6 in 6391 is 6000.
Ans. Many mathematical ideas make use of place value. It lays the groundwork for regrouping, multiplication, and other operations.
Ans. To enhance place value comprehension, manipulatives such as base-10 blocks, snap cubes, unfix cubes, beans, and so on are employed.