The local value of any digit in a number is the value of a digit depending on its place.
This concept is fundamental in understanding how numbers are constructed in positional numeral systems, like the decimal system we use daily. Unlike the face value of a digit, which is simply the value of the digit itself (e.g., the face value of 5 is always 5), the local value changes based on where the digit appears within a number.
Local Value vs. Face Value
The key difference lies in the digit's position.
- Local Value: Determined by the digit's value multiplied by the value of the place it occupies (ones place, tens place, hundreds place, etc.).
- Face Value: The intrinsic value of the digit itself, regardless of its position.
Think of it this way: in the number 555, the digit '5' appears three times. Its face value is always 5. However, its local value is different for each position:
- The '5' in the hundreds place has a local value of 500 (5 x 100).
- The '5' in the tens place has a local value of 50 (5 x 10).
- The '5' in the ones place has a local value of 5 (5 x 1).
This concept is explicitly stated in the reference: "The local value of any digit in a number is the value of a digit depending on its place. The face value of the digit in numeral is the value of digit itself, irrespective of its place in the numeral."
Example from the Reference
The provided reference gives a clear example:
- Number: 475240
- Focus Digit: 5
Let's analyze the values of the digit 5 in this number:
- Local Value of 5: The digit 5 is in the thousands place. The value of the thousands place is 1,000. Therefore, the local value of 5 is 5 * 1,000 = 5000.
- Face Value of 5: The value of the digit itself is simply 5.
This confirms the reference's statement: "The local value of 5 in 475240 is 5000. And the face value of 5 in 475240 is 5."
Understanding local value is crucial for performing arithmetic operations and grasping the structure of numbers in place-value systems.
