Chained division with small decimals: Evaluate 99.999 ÷ 0.99 ÷ 0.00991234 and select the closest option.

Introduction / Context:
A chained division by decimals is equivalent to multiplying by their reciprocals. Dividing by a number just under 1 increases the value slightly, and dividing by a very small number (around 0.01) increases it by around two orders of magnitude, guiding us toward the right scale of the answer.

Given Data / Assumptions:

• a = 99.999
• b = 0.99
• c = 0.00991234

Concept / Approach:
Compute sequentially: (99.999 / 0.99) ≈ 101.0, then divide that by c ≈ 0.0099, which is close to multiplying by ~101. The magnitude suggests a result near ten thousand. Choose the closest option accordingly.

Step-by-Step Solution:

Verification / Alternative check:
Back-of-the-envelope: 100 / (0.01) = 10000, and our inputs are slightly adjusted from these round anchors, so ~10,000 is very reasonable. The nearest option is 10,000.

Why Other Options Are Wrong:

• 100, 1000: too small by orders of magnitude.
• 100000: too large by about a factor of 10.
• 12000: closer than others but still farther than 10000 from the true ≈10190 when considering the coarse options.

Common Pitfalls:
Assuming that dividing by 0.99 reduces the value (it actually increases it), or mishandling decimal places in the tiny divisor 0.0099....

Final Answer:
10000