In the three digit number 103, what is the place value of the digit 0?

Introduction / Context:
This question tests basic understanding of place value in the decimal number system, specifically the role of the digit zero in a number like 103. Place value is a foundation for all further work in arithmetic and number operations, so it is important to distinguish between position (place) and actual contribution to the value of the number.

Given Data / Assumptions:
- The number given is 103.- It is a three digit number with digits 1, 0, and 3.- The digit 1 is in the hundreds place, 0 is in the tens place, and 3 is in the ones place.- We are asked for the place value of the digit 0.

Concept / Approach:
In the decimal place value system, the value of a digit depends on its position. The digit in the ones place is multiplied by 1, the digit in the tens place is multiplied by 10, and the digit in the hundreds place is multiplied by 100. More generally, a digit in the k th place from the right (starting with ones as first) has a place value equal to digit times 10^(k - 1). When the digit is zero, its place value is zero regardless of the place, because zero multiplied by any power of ten is still zero. Nevertheless, the zero still serves an important role as a placeholder to indicate that there are no tens in the number.

Step-by-Step Solution:
- Write the number 103 in expanded form.- 103 = 1 * 100 + 0 * 10 + 3 * 1.- The digit 1 in the hundreds place contributes 1 * 100 = 100 to the total.- The digit 0 in the tens place contributes 0 * 10 = 0 to the total.- The digit 3 in the ones place contributes 3 * 1 = 3 to the total.- Therefore, the place value of the digit 0 is 0.

Verification / Alternative check:
If the tens digit were not zero but some other digit, say 5, the number would be 153, and the tens digit would contribute 5 * 10 = 50. In 103, the absence of any tens is represented by 0 in the tens place, whose place value is 0. This shows that zero in a place always contributes zero to the total value but still influences how we interpret the other digits by shifting them into higher place positions.

Why Other Options Are Wrong:
- 100: This is the place value of the digit 1 in the hundreds place, not the digit 0.- 10: This is the place value factor for the tens place, but the digit itself is zero, so the product is 0.- 103: This is the value of the entire number, not the place value of a single digit.- 1: This is the place value of a digit in the ones place if that digit is 1, not the tens digit 0.

Common Pitfalls:
Some learners confuse the name of the place with the place value. The tens place always uses the factor 10, but if the digit there is 0, then the place value is 0. Another mistake is to think that zero can be ignored entirely, when in fact it is essential for correctly representing numbers like 103, where it ensures that the 1 remains in the hundreds place rather than shifting into the tens place.

Final Answer:
The place value of the digit 0 in 103 is 0.