In the numeral 967452, what is the difference between the place value and the face value of the digit 7?

Introduction / Context:
This problem checks understanding of place value and face value in the decimal number system. Knowing how the position of a digit alters its contribution to the overall number is a fundamental concept in arithmetic and is often tested in basic aptitude questions.

Given Data / Assumptions:
We are given the numeral 967452.We focus on the digit 7 within this number.We must find the difference between the place value and the face value of this digit.

Concept / Approach:
The face value of a digit is the digit itself, irrespective of its position in the number. The place value is the digit multiplied by the value of its positional place. For example, in a six digit number abcdef, the place values from left to right are hundred thousands, ten thousands, thousands, hundreds, tens and units. Once we identify the position of the digit 7 in 967452, we can compute its place value and then take the difference with its face value.

Step-by-Step Solution:
Step 1: Write the number with place labels: 9 (hundred thousands), 6 (ten thousands), 7 (thousands), 4 (hundreds), 5 (tens), 2 (units).Step 2: The digit 7 is in the thousands place.Step 3: The face value of 7 is simply 7.Step 4: The place value of 7 in the thousands place is 7 * 1000 = 7000.Step 5: Compute the difference between place value and face value: 7000 − 7 = 6993.

Verification / Alternative check:
We can also write the number 967452 as a sum of place values: 9 * 100000 + 6 * 10000 + 7 * 1000 + 4 * 100 + 5 * 10 + 2. From this expression, it is clear that the contribution of the digit 7 is 7 * 1000 = 7000. Subtracting the face value 7 again gives 6993, confirming the result.

Why Other Options Are Wrong:
The alternative values 6393, 5831 and 6339 do not correspond to the difference between 7000 and 7. They might arise from mistaken place values, for example by mis-locating the digit 7 in the tens or hundreds place. Since the correct place value is exactly 7000, only 6993 fits the required difference.

Common Pitfalls:
A common error is to misread the position of the digit 7, especially in large numbers. Some learners also confuse place value with simply writing the digit followed by zeros without counting the correct position. Carefully mapping each digit to its place (units, tens, hundreds, thousands and so on) helps avoid these mistakes.

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