Question

Find the difference between the place value and the face value of the digit 7 in the number 4782.

• A. 700
• B. 7
• C. 693
• D. 782
• E. 707

Hint:

Place value changes depending on where the digit sits in the number, but face value is always just the digit itself. Always double-check the positional unit (ones, tens, hundreds) before subtracting.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem asks for the mathematical difference between two distinct mathematical properties of a digit within a number: its place value and its face value.


Step 2: Key Formula or Approach:
Place value = Face value \times Numerical value of its position (e.g., 10, 100, 1000).
Face value = The digit itself, irrespective of its position.


Step 3: Detailed Explanation:
The given number is 4782.
First, identify the position of the digit 7. It is situated in the hundreds place.
Therefore, the place value of 7 is: \[ 7 \times 100 = 700 \] The face value of any digit is simply the value of the digit itself.
Therefore, the face value of 7 is \(7\).
The difference between the place value and the face value is: \[ 700 - 7 = 693 \]

Step 4: Final Answer:
The difference is 693.