Solve for a missing factor in a decimal equation Find ? such that 0.8 × ? = 0.0004.

Introduction / Context:
This is a straightforward equation with decimals. The idea is to isolate the unknown by dividing both sides by 0.8 and to place the decimal point correctly. It reinforces the link between division by 8/10 and multiplying by 10/8.

Given Data / Assumptions:

• 0.8 × ? = 0.0004.
• 0.8 = 8/10.

Concept / Approach:
Divide both sides by 0.8: ? = 0.0004 / 0.8. Since 0.8 = 8/10, dividing by 0.8 is the same as multiplying by 10/8. This converts the decimal division into a simple fraction operation.

Step-by-Step Solution:
? = 0.0004 / 0.8.Rewrite 0.8 as 8/10: ? = 0.0004 × (10/8).Compute: 0.0004 × 10 = 0.004; then 0.004 / 8 = 0.0005.

Verification / Alternative check:
Multiply back: 0.8 × 0.0005 = 0.0004, confirming the solution.

Why Other Options Are Wrong:
.005 and .5 are too large by factors of 10^1 and 10^3 respectively; .00005 is too small by 10; 0.0004 is the right-hand side, not the missing factor.

Common Pitfalls:
Moving the decimal in the wrong direction when dividing by a number less than 1; forgetting that dividing by 0.8 increases the value.

Final Answer:
.0005