Discussion
Find the third proportional to 3, 0.09.
Answer: A
The third proportional is 0.0027. If c is the third proportional to a and b, then a : b = b : c, which gives c as the square of b divided by a.
\[ c = \frac{b^2}{a} = \frac{0.09^2}{3} \]
\[ c = \frac{0.0081}{3} = 0.0027 \]
Check: 3 : 0.09 and 0.09 : 0.0027 both equal 100 : 3, since 0.09 divided by 3 is 0.03 and 0.0027 divided by 0.09 is 0.03. The options 0.0018, 0.009 and 0.003 give a different ratio for the second pair, so they are not the third proportional.
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