In the three digit number 475, what is the place value of the digit 4?

Introduction / Context:
This question tests understanding of place value in the decimal number system. Every digit in a number has two different ideas attached to it: its face value (the digit itself) and its place value (the value contributed by the digit due to its position in the number). Many students confuse these two concepts, especially when working with three digit and larger numbers. Here we analyse the number 475 and focus on the digit 4 to determine its correct place value.

Given Data / Assumptions:

• The number given is 475, which is a three digit number.
• The digit of interest is 4, which is the leftmost digit of 475.
• We are working in the standard base 10 (decimal) number system.
• We must find the place value of the digit 4, not just its face value.

Concept / Approach:
In the decimal system, each position represents a power of 10. From right to left, the places are: units (10^0), tens (10^1), hundreds (10^2), thousands (10^3), and so on. The face value of a digit is simply the digit itself, but the place value is digit * (value of the position). In a three digit number ABC, A is in the hundreds place, B in the tens place and C in the units place. Therefore A contributes A * 100 to the number, B contributes B * 10, and C contributes C * 1.

Step-by-Step Solution:
Step 1: Write the number 475 in expanded form using place values.Step 2: 475 can be written as 4 * 100 + 7 * 10 + 5 * 1.Step 3: The digit 4 is in the hundreds place, so its place value is 4 * 100.Step 4: Compute 4 * 100 = 400.Step 5: Therefore the place value of the digit 4 in the number 475 is 400.

Verification / Alternative check:
A quick check is to compare what happens if we remove the digit 4. If 475 becomes 075 or just 75, the difference between 475 and 75 is 400. This difference of 400 is exactly what the 4 in the hundreds place contributes, confirming that the place value of 4 is 400. This is another way to see that the leftmost digit in a three digit number represents hundreds.

Why Other Options Are Wrong:
Option 4: This is the face value of the digit, not its place value. It ignores position.Option 475: This is the value of the entire number, not just the digit 4.Option 40: This would be the place value if 4 were in the tens place, but in 475 it is not.Option 0.4: This corresponds to a decimal place value (tenths), which does not apply here.

Common Pitfalls:
Students often confuse face value and place value, especially for leading digits. Another frequent mistake is to think that the value of a digit is always just the digit itself, without taking into account its position. Some also mix up tens and hundreds place values, writing 40 instead of 400. Remember that each step left in a whole number multiplies the place value by 10. Careful reading of the question, especially the words "place value", is essential.

Final Answer:
The place value of the digit 4 in the number 475 is 400.