What is the average of the decimal numbers four tenths and five thousandths?

Introduction:
This problem checks your understanding of decimal numbers written in words and your ability to compute a simple arithmetic average. You must correctly convert the verbal descriptions four tenths and five thousandths into decimal form, then use the formula for the average of two numbers.

Given Data / Assumptions:
- One number is four tenths. - The other number is five thousandths. - We are asked to find the average of these two numbers.

Concept / Approach:
Four tenths means 4 parts out of 10, which is 4/10. Five thousandths means 5 parts out of 1000, which is 5/1000. After converting both to decimal form, we apply the average formula for two numbers: average = (number1 + number2) / 2. Careful handling of decimal places is important to avoid mistakes.

Step-by-Step Solution:
Step 1: Convert four tenths to decimal form: 4 tenths = 4/10 = 0.4. Step 2: Convert five thousandths to decimal form: 5 thousandths = 5/1000 = 0.005. Step 3: Add the two numbers: 0.4 + 0.005 = 0.405. Step 4: The average of two numbers is their sum divided by 2. Step 5: Compute 0.405 / 2. Step 6: 0.405 divided by 2 equals 0.2025. Step 7: Therefore, the required average = 0.2025.

Verification / Alternative Check:
We can verify the division 0.405 / 2 by converting 0.405 to a fraction: 0.405 = 405/1000. Dividing by 2 is the same as multiplying by 1/2, so we get 405/1000 * 1/2 = 405/2000. Simplifying 405/2000 by dividing numerator and denominator by 5 gives 81/400. As a decimal, 81/400 = 0.2025. This matches our earlier result.

Why Other Options Are Wrong:
Option 0.045 comes from incorrectly treating one of the numbers or from dividing by 10 instead of 2. Option 0.205 and 0.225 are close numbers but they do not match the exact result of 0.405 divided by 2. Option 0.4005 wrongly suggests some misplacement of the decimal point when adding or averaging the numbers.

Common Pitfalls:
Students often confuse tenths with thousandths or misplace the decimal point when converting from fractions to decimals. Another frequent error is to add correctly but then divide by 10 or some other number instead of 2. Writing the fractions explicitly before converting to decimals can help prevent these mistakes.

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