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Express the product of \(3.2\times 10^{6}\) and \(4.1\times 10^{-1}\) in the standard form.
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Question

Express the product of \(3.2\times 10^{6}\) and \(4.1\times 10^{-1}\) in the standard form.

Answer

Product of \(3.2\times 10^{6}\) and \(4.1\times 10^{-1}\),
\(=3.2\times 10^{6}\times 4.1\times 10^{-1}\)
\(=(3.2\times 4.1)\times 10^{(6-1)}\) [As \(a^x\times a^y=a^{(x+y)}\)]
\(=13.12\times 10^5\)
Multiplying and dividing by \(10\) to represent in standard form, we get
\(13.12\times 10^5\times \frac{10}{10}\)
\(=\frac{13.12}{10}\times10^{(5+1)}\)
\(=1.312\times 10^6\).
Hence, the product of \(3.2\times 10^{6}\) and \(4.1\times 10^{-1}\) in the standard form is \(1.312\times 10^6\).
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