Difficulty: Easy
Correct Answer: 0.0009
Explanation:
Introduction / Context:
This question checks your understanding of decimal multiplication and division, two very common operations in aptitude and school mathematics. Many students know the rules in theory but still misplace the decimal point in practice. Here, you are asked to square 0.3 and then divide the result by 100, so you must clearly track how many decimal places are created at each step.
Given Data / Assumptions:
Concept / Approach:
When you multiply decimals, you multiply as whole numbers first and then count the total number of decimal places. When you divide by 10, 100, 1000 and so on, you move the decimal point to the left by as many zeros as the divisor has. This question combines both ideas in a simple setting and rewards careful handling of the decimal point rather than speed alone.
Step-by-Step Solution:
Verification / Alternative check:
You can also treat everything as fractions. Since 0.3 = 3/10, we have (3/10)^2 = 9/100. Dividing by 100 means multiplying by 1/100, so the result is 9/10000. Written as a decimal, 9/10000 is 0.0009, which matches the previous method and confirms the answer.
Why Other Options Are Wrong:
The value 0.09 is only (0.3)^2, before dividing by 100. The value 0.009 corresponds to dividing by 10 instead of 100. The value 0.9 ignores the squaring and division steps, and 0.0003 comes from incorrect counting of decimal places after division.
Common Pitfalls:
A very common mistake is to forget that 0.3 squared has two decimal places, not one, leading to 0.9. Another mistake is to move the decimal only one place left when dividing by 100, which would give 0.009. Carefully counting decimal places at each step prevents these errors.
Final Answer:
The correct value of the given decimal expression is 0.0009.
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