What is the average (arithmetic mean) of the decimal numbers four tenths and five thousandths?

Introduction / Context:
This problem checks your comfort with decimal notation and basic averages. You are given two numbers expressed in words as decimal fractions and asked to find their average. The key skills are to correctly convert the verbal expressions into numerical decimals and then apply the standard formula for the arithmetic mean of two numbers.

Given Data / Assumptions:

• First number is four tenths.
• Second number is five thousandths.
• We must compute the average of these two decimal numbers.
• We assume standard decimal place value: tenths, hundredths, thousandths and so on.

Concept / Approach:
The average (or arithmetic mean) of two numbers a and b is given by:
Average = (a + b) / 2. We first translate the words into decimal form: four tenths becomes 0.4 and five thousandths becomes 0.005. Then we add these decimals and divide by 2. Careful handling of decimal places ensures we get the exact correct value.

Step-by-Step Solution:
Step 1: Convert four tenths into decimal form. Four tenths = 4 / 10 = 0.4. Step 2: Convert five thousandths into decimal form. Five thousandths = 5 / 1000 = 0.005. Step 3: Add the two decimals: 0.4 + 0.005. Step 4: Write 0.4 as 0.400 to make the place values line up: 0.400 + 0.005 = 0.405. Step 5: Now compute the average: (0.4 + 0.005) / 2 = 0.405 / 2. Step 6: Divide 0.405 by 2: 0.405 / 2 = 0.2025. Step 7: Therefore, the average of four tenths and five thousandths is 0.2025.

Verification / Alternative check:
We can verify by working with fractions instead of decimals. Four tenths = 4 / 10 and five thousandths = 5 / 1000. Convert both to a common denominator of 1000: 4 / 10 = 400 / 1000. Then the sum is (400 / 1000) + (5 / 1000) = 405 / 1000. The average is (405 / 1000) / 2 = 405 / 2000. Dividing numerator and denominator by 5 gives 81 / 400, which in decimal form is 0.2025. This matches the earlier decimal calculation exactly.

Why Other Options Are Wrong:
The options 25002 and 2502 clearly ignore the decimal place values and look like misinterpretations of the numbers as whole integers. The option 0.225 would be correct if the sum was 0.45, which would come from misreading five thousandths as 0.05 instead of 0.005. The option 'none of these' is not correct because 0.2025 is already present among the choices. Therefore, 0.2025 is the only correct answer.

Common Pitfalls:
A common mistake is confusing five thousandths (0.005) with five hundredths (0.05). Another frequent error is to add the decimals incorrectly, for example writing 0.4 + 0.005 = 0.45. Students also sometimes forget to divide by 2 after adding the two numbers. Paying attention to place values and following the operations in sequence helps avoid these errors.

Final Answer:
The average of four tenths and five thousandths is 0.2025.