Which of the following has the smallest value?（ ）

A

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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 \((A).\)

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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