Handle nested decimals and a complex division: Compute (.23 − .023) / (.0023 / 23) and choose the exact value.

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:

Verification / 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