Essential Properties and Real-Life Applications of Value
In mathematics, the value may refer to a variety of closely connected notions.
In general, any particular mathematical entity can have a mathematical meaning. In elementary mathematics, this is most commonly a number – for example, a real number likeor an integer such as 42. The value of a vector or constant is the integer or other mathematical entity attributed to it. The value of the mathematical equation is the result of the formula defined in this expression when the variables and constants in the expression are given values.
The value of a function, given the value(s) assigned to its argument(s), is the number assumed by the function for that argument value. If the variable, expression, or function just assumes real values, it is called real-value. In the same way, a complex-valued variable, expression, or function just assumes complex values.
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Place Value
Per digit in a number has a position value in math. Place value can be defined as the value expressed by a digit in a number based on its location in a number. A place value map will help us find and compare the place value of the digits in numbers across millions. The place value of the digit increases by 10 times as we step left on the place value map and decreases by 10. The place value of the digit increases by 10 times as we move left on the place value map and decreases by 10 times as we move right.
Properties of Place Value:
The place value of each one-digit integer is the same as and equal to its face value.
In a two-digit number, the place value of the ten-digit digit is 10 times the digit.
In the number 562, digit 2 is at one’s place, 6 is at ten’s place, and the digit 5 is at hundred’s place.
It is also the common rule that the digit has its place value as the product of the digit and the place value of the digit.
Face Value
The value of the face in Maths is the value of the digit in a number. We know any number has a digit. Numbers can be one-digit, two-digit, three-digit, or more than three-digit. There are countless quantities here. Each digit has its place value as well as its face value. The value of the digit in a number is the value of the digit itself. This value is the same anywhere it's put in a number.
What is the Value of a Number?
Each digit has a fixed place called its spot.
● Each digit has a value, based on its location, called the place value of the digit.
● The face value of the digit at some position in the given number is the value of the digit itself.
● The Number Value of the digit = (the face value of the digit) × (value of the place)
Solved Examples
1. What is the Value of 4 in 65437?
Ans:
4 is in hundred’s place. Therefore to find the value of 4 in 65437 we will use the following formula:
Number Value of the digit = (the face value of the digit) × (value of the place)
= 4 x 100
Ans =400
2. What is the Value of 6 in 4,967,313?
Ans:
6 is at the ten-thousands place. Therefore to find the value of 6 in 4,967,313 we will use the following formula:
Number Value of the digit = (the face value of the digit) × (value of the place)
= 6 x 10,000
Ans = 60,000
3. Find The Value of 4 in 3,453,125?
Ans:
4 is at the hundred-thousands place. Therefore to find the value of 4 in 3,453,125 we will use the following formula:
Number Value of the digit = (the face value of the digit) × (value of the place)
= 4 x 1,00,000
Ans = 4,00,000
4. What is the Place Value and Value of 2 in 4,354,521?
Ans:
2 is at ten’s place. Therefore to find the value of 2 in 4,354,521 we will use the following formula:
Number Value of the digit = (the face value of the digit) × (value of the place)
= 2 x 10
Ans = 20
FAQs on Understanding Value in Mathematics
1. What does 'value' mean in mathematics?
In mathematics, 'value' can have two main meanings. Firstly, it can be the result of a calculation, like the value of 5 + 10 is 15. Secondly, and more commonly in the context of numbers, it refers to how much a digit is worth based on its position in a number. This is known as its place value. For example, in the number 250, the digit '2' has a value of two hundred, while the digit '5' has a value of fifty.
2. How is the value of a specific digit determined in a number? Explain with an example.
The value of a digit is determined by its place or position within a number. Each position has a specific value, such as ones, tens, hundreds, thousands, and so on. To find the value of a digit, you multiply the digit by the value of its position. For example, in the number 3,475:
The digit 5 is in the ones place, so its value is 5 x 1 = 5.
The digit 7 is in the tens place, so its value is 7 x 10 = 70.
The digit 4 is in the hundreds place, so its value is 4 x 100 = 400.
The digit 3 is in the thousands place, so its value is 3 x 1000 = 3,000.
3. What is the difference between face value and place value?
The difference between face value and place value is a fundamental concept. Face value is simply the digit itself, regardless of its position. Place value is the value of the digit based on its position in the number. For instance, in the number 892:
The digit '9' has a face value of 9.
The digit '9' has a place value of 90 (since it is in the tens place).
The face value never changes, but the place value changes with the digit's position.
4. How do periods help in understanding the value of large numbers?
Periods are groups of digits separated by commas that make large numbers easier to read and understand. In the Indian Numbering System, periods group digits into ones, thousands, lakhs, and crores. In the International Numbering System, they are grouped into ones, thousands, millions, and billions. For example, the number 54389012:
In the Indian system, it is written as 5,43,89,012 (Five crore, forty-three lakh, eighty-nine thousand, twelve).
In the International system, it is written as 54,389,012 (Fifty-four million, three hundred eighty-nine thousand, twelve).
Using periods helps us quickly identify the value of each part of the number.
5. How does the concept of value apply to digits after a decimal point?
The concept of place value extends to digits to the right of the decimal point, representing values less than one. Each position has a fractional value. For the number 45.68:
The digit 6 is in the tenths place, so its value is 6/10 or 0.6.
The digit 8 is in the hundredths place, so its value is 8/100 or 0.08.
The further a digit is to the right of the decimal, the smaller its value becomes.
6. Why is understanding the value of digits important in real life?
Understanding the value of digits is crucial for many real-life tasks. It helps in:
Handling Money: Knowing the difference between ₹10, ₹100, and ₹1000 is a direct application of place value.
Measurement: Correctly reading measurements of length (e.g., 1.5 metres), weight (e.g., 2.75 kg), or volume depends on understanding decimal values.
Data Interpretation: When reading statistics, like population figures or financial reports, understanding place value helps grasp the magnitude of the numbers involved.
7. How does the value of a number change when a digit moves one place to the left or right?
Our number system is a base-10 system. This means the value of a position is 10 times the value of the position to its immediate right. Consequently:
When a digit moves one place to the left, its value becomes 10 times greater. For example, when 7 moves from the ones place (value 7) to the tens place (value 70), its value is multiplied by 10.
When a digit moves one place to the right, its value becomes 10 times smaller (or is divided by 10). For example, when 4 moves from the hundreds place (value 400) to the tens place (value 40), its value is divided by 10.
