Step 1: Understanding the Question:
The question requires us to identify two specific values for the digit '7' in the given number 4782: its "place value" and its "face value".
The final objective is to calculate the mathematical difference (subtraction) between these two values.
Step 2: Key Formula or Approach:
Face Value: The face value of a digit is the value of the digit itself, regardless of its position in the number.
Place Value: The place value of a digit depends on its position in the number (units, tens, hundreds, thousands, etc.). It is calculated as \(\text{Digit} \times \text{Value of the place}\).
Step 3: Detailed Explanation:
Analyzing the number 4782: Let's break down the positions of the digits in the number 4782:
- 2 is in the Units place (\(2 \times 1\))
- 8 is in the Tens place (\(8 \times 10\))
- 7 is in the Hundreds place (\(7 \times 100\))
- 4 is in the Thousands place (\(4 \times 1000\))
Finding the Place Value of 7: Since the digit 7 is at the hundreds position, its place value is: \[7 \times 100 = 700\]
Finding the Face Value of 7: The face value is simply the digit itself. Therefore, the face value of 7 is 7.
Calculating the Difference: We subtract the face value from the place value: \[700 - 7 = 693\]
Conceptual Importance: Understanding the difference between these two values is fundamental to the decimal number system. While the face value is static, the place value is dynamic and provides the magnitude of the number.
Step 4: Final Answer:
The difference between the place value and face value of the digit 7 in 4782 is 693.