In the two digit number 64, what is the place value of the digit 6?

Introduction / Context:
This is a very basic problem from the topic of number systems. It tests understanding of the concept of place value in a two digit number. Even though the question looks simple, place value is a fundamental concept that underlies many more advanced numerical operations and decimal representations.

Given Data / Assumptions:
- The number under consideration is 64.
- It is a two digit number with 6 in the tens place and 4 in the units place.
- We are asked specifically for the place value of the digit 6 in this number.

Concept / Approach:
In a two digit number, the rightmost digit is in the units place and the left digit is in the tens place. The place value of a digit is the digit multiplied by the value of its position. In the tens place, the position value is 10, so the place value of the digit is that digit multiplied by 10. In the units place, the position value is 1, so the place value is the digit itself.

Step-by-Step Solution:
Step 1: Identify the digits and their positions in the number 64. The digit 6 is in the tens place and the digit 4 is in the units place.Step 2: The value of the tens place is 10. Therefore, the place value of a digit in the tens place is digit * 10.Step 3: For the digit 6 in the tens place, the place value is 6 * 10.Step 4: Compute the product: 6 * 10 = 60.Step 5: Thus, the place value of the digit 6 in the number 64 is 60.

Verification / Alternative check:
We can express 64 in expanded form based on place values. The number 64 can be written as 60 + 4, which is 6 * 10 + 4 * 1. Here, 6 * 10 represents the contribution of the digit 6 in the tens place, which is exactly 60. This confirms that the place value of 6 in 64 is 60.

Why Other Options Are Wrong:
The option 6 represents only the face value of the digit, not the place value. The option 64 represents the whole number, not the contribution from the tens place. The option 10 is just the place value of the position, not of the digit itself, and 600 is too large and would correspond to 6 in the hundreds place. Therefore, only 60 correctly represents the place value of 6 in 64.

Common Pitfalls:
Some learners confuse face value with place value and answer 6 instead of 60. Others may misinterpret the question and think it asks for the overall value of the number. Remember that face value is the digit itself, while place value is the digit multiplied by the value of its position in the number. Clear understanding of this distinction avoids such errors.

Final Answer:
The place value of the digit 6 in 64 is 60.