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Question

Which of the following has the smallest value?( )
A. \(0.0002\)
B. \(\frac {2}{1000}\)
C. \(\frac {(0.2)^{2}}{2}\)
D. \(\frac {2}{100}\div 0.01\)

Answer

A
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Solution

Check it by options
Make same denominator of all given expressions, and compare them to get smallest value.
\((A)\) \(0.0002\)
\(=0.0002\times\frac{10000}{10000}\)
\(=\frac{2}{10000}\)
\((B)\) \(\frac {2}{1000}\)
\(=\frac {2}{1000}\times\frac{10}{10}\)
\(=\frac{20}{10000}\)
\((C)\) \(\frac {(0.2)^{2}}{2}\)
\(=\frac {0.2\times0.2}{2}\times\frac{10000}{10000}\)
\(=\frac {0.1\times0.2\times10000}{10000}\)
\(=\frac {200}{10000}\)
\((D)\) \(\frac {2}{100}\div 0.01\)
\(=\frac {2}{100}\times\frac{1}{0.01}\) \([\because a\div b=a\times\frac{1}{b}]\)
\(=\frac {2}{100}\times \frac{100}1\times\frac{10000}{10000}\)
\(=\frac {20000}{10000}\)
As, \(\frac{2}{10000}<\frac{20}{10000}<\frac{200}{10000}<\frac{20000}{10000}\)
Thus, correct option is \((A).\)
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