If 40 is equal to 0.05 percent of a number x, what is the value of x?

Introduction / Context:
This question focuses on converting a very small percentage into its decimal form and then using it to find the original number. It reinforces the relationship between percentages, fractions, and decimals, which is fundamental in all percentage based problems.

Given Data / Assumptions:
0.05 percent of x equals 40. We need to find the value of x. All values are positive real numbers.

Concept / Approach:
A percentage can be written as a fraction out of 100. Thus 0.05 percent is 0.05 / 100. That can be converted to a decimal multiplier. Once we express 0.05 percent as a decimal, we can write the equation (0.05 / 100) * x = 40, and then solve for x by dividing 40 by this small factor.

Step-by-Step Solution:
We are told 0.05 percent of x = 40. Convert 0.05 percent to decimal form. 0.05 percent = 0.05 / 100. Compute 0.05 / 100 = 0.0005. So the equation becomes 0.0005 * x = 40. To find x, divide both sides by 0.0005. Thus x = 40 / 0.0005. Compute 40 / 0.0005 = 40 * (1 / 0.0005) = 40 * 2000 = 80000. Therefore x = 80000.

Verification / Alternative check:
Check by forward calculation. Compute 0.05 percent of 80000. First find 1 percent of 80000 which is 800. Then 0.05 percent is 0.05 times 800 which equals 40. This matches the given value. Another quick way is to note that 0.05 percent is one twentieth of 1 percent, and the numbers remain consistent.

Why Other Options Are Wrong:
If x were 8000, then 0.05 percent of 8000 would be 4. For 800, 0.05 percent is 0.4. For 80, it is 0.04. For 40000, 0.05 percent equals 20. None of these equal 40. Only x equal to 80000 yields 40 as 0.05 percent of x.

Common Pitfalls:
A common mistake is to treat 0.05 percent as 0.05 or 5 percent instead of 0.0005. Misplacing decimal points when dealing with very small percentages can lead to large errors in the final answer. Carefully converting percent to decimal and checking the order of magnitude helps prevent such errors.

Final Answer:
The value of x for which 40 is 0.05 percent of x is 80000.