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# The mass of one oxygen molecule is $5.3 \times 10^{-23}$ gram. Find the mass of 20,000 molecules of oxygen. Express the answer in scientific notation.

Solution

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Multiply the mass of one oxygen molecule, $5.3\times 10^{-23}$ gram by 20,000 or $2\times 10^4$: $(5.3\times 10^{-23})\times (2\times 10^4)$ Use the associative property and commutative property of multiplication to regroup factors:

$=(5.3\times 2)\times (10^{-23}\times 10^4)$

Use the product rule for exponents: $b^m\cdot b^n=b^{m+n}$

\begin{align*} &= 10.6 \times 10^{-23+4}\\ &= 10.6 \times 10^{-19} \end{align*}

This is not written in scientific notation since the factor 10.6 is not between 1 and 10 so we rewrite as:

\begin{align*} &=(1.06\times 10^{1})\times 10^{-19}\\ &=1.06\times 10^{1+(-19)}\\ &= \color{#c34632}1.06\times 10^{-18}\text{ gram} \end{align*}

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