Handle nested decimals and a complex division: Compute (.23 − .023) / (.0023 / 23) and choose the exact value.
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A0.207
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B207
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C2070
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D0.0207
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E20.7
Answer
Correct Answer: 2070
Explanation
Introduction / Context:This problem combines decimal subtraction with a division by a small decimal ratio, testing careful manipulation of place values and reciprocals.
Given Data / Assumptions:
- Numerator: 0.23 − 0.023.
- Denominator: 0.0023 / 23.
- Perform exact arithmetic (no rounding required).
Concept / Approach:First simplify the numerator. Then recognize that dividing by a small number is equivalent to multiplying by its reciprocal; compute the denominator exactly to avoid compounding decimal errors.
Step-by-Step Solution:
Numerator: 0.23 − 0.023 = 0.207Denominator: 0.0023 / 23 = 0.0001 (since 23 × 0.0001 = 0.0023)Overall value = 0.207 / 0.0001 = 2070Verification / Alternative check:Rewrite the compound fraction: (0.23 − 0.023) * (23 / 0.0023) = 0.207 * 10000 = 2070, the same result.
Why Other Options Are Wrong:0.207 and 0.0207 ignore the denominator’s effect. 207 under-multiplies by a factor of 10. 20.7 is still short by two orders of magnitude.
Common Pitfalls:Miscomputing 0.0023 / 23 or moving the decimal point incorrectly when dividing by a ten-thousandth.
Final Answer:2070