In the six digit numeral 967452, the digit 7 is in the thousands place. What is the difference between the place value of this digit and its face value?

Introduction:
This question checks your understanding of the concepts of face value and place value of a digit in a numeral. These are basic ideas in number systems and positional notation, which are often tested in aptitude exams.

Given Data / Assumptions:

• The numeral is 967452.
• We focus on the digit 7 in this numeral.
• We must find the difference: (place value of 7) − (face value of 7).

Concept / Approach:
The face value of a digit is simply the digit itself, regardless of where it appears in the number. The place value, however, depends on the position of the digit. In a six digit number, the positions from right to left are units, tens, hundreds, thousands, ten thousands, and lakhs. The value of a digit is the digit multiplied by the positional multiplier corresponding to its place.

Step-by-Step Solution:
Write the number with place labels: 967452. From right to left: 2 is units, 5 is tens, 4 is hundreds, 7 is thousands, 6 is ten thousands, 9 is lakhs. So the digit 7 is in the thousands place. Face value of 7 = 7. Place value of 7 = 7 × 1000 = 7000. We need the difference between place value and face value: Difference = 7000 − 7 = 6993.

Verification / Alternative check:
You can also expand the full number: 967452 = 9 × 100000 + 6 × 10000 + 7 × 1000 + 4 × 100 + 5 × 10 + 2. Here the contribution of the digit 7 is clearly 7000. Subtracting its face value 7 again gives 6993, confirming our earlier computation.

Why Other Options Are Wrong:
The values 6393, 5831, and 6339 would correspond to incorrect place values such as 7000 being misread, wrong subtraction, or confusion about the position of the digit in the number. None of these arise from correctly identifying 7 as the thousands digit and performing the subtraction 7000 − 7.

Common Pitfalls:
Learners sometimes mistake face value for place value and answer 7000 or 7 directly, ignoring the requested difference. Others misidentify the place, thinking 7 is in the ten thousands or hundreds place. Carefully counting positions from the right helps avoid such errors.

Final Answer:
The difference between the place value and face value of the digit 7 in 967452 is 6993.