Discussion
If \(\frac{1}{2.5} = 0.4\), then what is the value of \(\frac{1}{0.000025}\)?
Answer: B
The value is 40000. Since \(\frac{1}{2.5} = 0.4\), write \(0.000025 = 2.5 \times 10^{-5}\). Then
\[ \frac{1}{0.000025} = \frac{1}{2.5} \times 10^{5} \]\[ = 0.4 \times 100000 = 40000 \]4000 and 400 come from using the wrong power of ten, and 400000 comes from one power too many.
Another way: 0.000025 is 25 millionths, and \(\frac{1}{25 \times 10^{-6}} = \frac{10^{6}}{25} = 40000\). This agrees with the first method, which makes the answer 40000 and rules out 4000 and 400 (too small by factors of ten and a hundred) and 400000 (ten times too large).
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