Determine the place value of the digit 3 in the decimal number 0.07359. Express the place value as a fraction of a unit.

Introduction / Context:
Understanding place value to the right of the decimal point is fundamental. Each position represents a reciprocal power of 10: tenths, hundredths, thousandths, ten-thousandths, and so on. This question asks you to identify the exact place value for a specific digit in a given decimal.

Given Data / Assumptions:

• Number: 0.07359
• Digit of interest: 3

Concept / Approach:
List each digit’s place moving right from the decimal: tenths (10^-1), hundredths (10^-2), thousandths (10^-3), ten-thousandths (10^-4), hundred-thousandths (10^-5). Identify where the 3 sits in this sequence and express its place value as a fraction of a unit.

Step-by-Step Solution:
0.07359 has digits after the decimal as: 0 (tenths), 7 (hundredths), 3 (thousandths), 5 (ten-thousandths), 9 (hundred-thousandths).The 3 is in the thousandths place, so its place value is 3 × (1/1000) = 3/1000.

Verification / Alternative check:
Write 0.07359 as a sum: 7/100 + 3/1000 + 5/10000 + 9/100000. The coefficient of 3 is clearly 1/1000.

Why Other Options Are Wrong:

• 3: This is the face value, not place value.
• 3/100 and 3/10000 and 3/100000: These correspond to hundredths, ten-thousandths, and hundred-thousandths, not the position of 3 here.

Common Pitfalls:
Miscounting decimal places, especially when a zero follows the decimal before non-zero digits.

Final Answer:
3/1000