Consider the number 43403. The digit 3 appears twice in this number, in different places. What is the difference between the local (place) values of the two 3s in 43403?

Introduction / Context:
This arithmetic reasoning question tests understanding of the concept of local or place value of digits in a number. The digit 3 appears in two different positions in the number 43403, and each position corresponds to a different place value. The problem asks for the numerical difference between these two place values.

Given Data / Assumptions:

• The number under consideration is 43403.
• The digits from left to right are 4, 3, 4, 0, and 3.
• The left 3 is in the thousands place, and the right 3 is in the ones place.
• Local value means digit multiplied by the value of its place (ones, tens, hundreds, thousands, and so on).

Concept / Approach:
In the decimal place value system, the rightmost position is the ones place, then tens, hundreds, thousands, and higher powers of 10 moving left. The place value of a digit equals that digit multiplied by 10 raised to the power corresponding to its position. The difference between the local values of the two 3s is simply the larger place value minus the smaller place value.

Step-by-Step Solution:
Step 1: Write the number 43403 and identify the positions of the digit 3. One 3 is the second digit from the left, the other 3 is the last digit on the right. Step 2: Determine the place of the left 3. From right to left, the positions are ones (3), tens (0), hundreds (4), thousands (3), ten thousands (4). So the left 3 is in the thousands place. Step 3: The local value of the left 3 is 3 * 1000 = 3000. Step 4: Determine the place of the right 3. It is in the ones place. Step 5: The local value of the right 3 is 3 * 1 = 3. Step 6: The difference between the local values is 3000 - 3 = 2997.

Verification / Alternative check:
You can rewrite 43403 as 4 * 10^4 + 3 * 10^3 + 4 * 10^2 + 0 * 10^1 + 3 * 10^0. The two 3s appear as 3 * 10^3 and 3 * 10^0. Their values are 3,000 and 3 respectively. Subtracting gives 3,000 - 3 = 2,997, reinforcing the earlier calculation.

Why Other Options Are Wrong:
Option A 0 would mean the two place values are equal, which is clearly not true. Option B 3,030 and option C 3,003 may come from adding or otherwise confusing the positions, but they do not represent the difference 3000 - 3. Only 2,997 equals the correct subtraction.

Common Pitfalls:
A common mistake is to confuse digit value with place value. The digit value of both 3s is 3, but their local values differ because of their positions. Another error is misidentifying the positions in the number, especially when counting from the wrong side. Always count places from the rightmost digit as ones, then tens, hundreds, and so on.

Final Answer:
The difference between the local values of the two 3s is 2,997.