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A sample of microbes weighs 50 mg. There are approximately 2.5 × 106 microbes in the sample. What is the approximate mass of each microbe expressed using scientific notation in grams.

 May 7, 2015

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 #1
avatar+25274 
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A sample of microbes weighs 50 mg. There are approximately 2.5 × 106 microbes in the sample. What is the approximate mass of each microbe expressed using scientific notation in grams.

$$\small\text{$
\begin{array}{lcl}
\mathbf{\dfrac{50~mg}{2.5\cdot 10^6~microbes} \cdot \dfrac{1~g}{1000~mg} } \\\\
\mathbf{ =\dfrac{50}{2.5\cdot 10^6\cdot 1000} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =\dfrac{50}{2.5\cdot 10^6\cdot 10^3} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =\dfrac{50}{2.5\cdot 10^9 } \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =\dfrac{50}{2.5 } \cdot 10^{-9} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =20 \cdot 10^{-9} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =20 \cdot \dfrac{ng}{ microbe } } \qquad ng = $ Nano gram$
\end{array}\\
$}}$$

the approximate mass of each microbe  is 20 ng (Nano gram) or $$\small{\text{$20 \cdot 10^{-9} ~g$}}$$

.
 May 7, 2015
 #1
avatar+25274 
+5
Best Answer

A sample of microbes weighs 50 mg. There are approximately 2.5 × 106 microbes in the sample. What is the approximate mass of each microbe expressed using scientific notation in grams.

$$\small\text{$
\begin{array}{lcl}
\mathbf{\dfrac{50~mg}{2.5\cdot 10^6~microbes} \cdot \dfrac{1~g}{1000~mg} } \\\\
\mathbf{ =\dfrac{50}{2.5\cdot 10^6\cdot 1000} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =\dfrac{50}{2.5\cdot 10^6\cdot 10^3} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =\dfrac{50}{2.5\cdot 10^9 } \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =\dfrac{50}{2.5 } \cdot 10^{-9} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =20 \cdot 10^{-9} \cdot \dfrac{g}{ microbe } } \\\\
\mathbf{ =20 \cdot \dfrac{ng}{ microbe } } \qquad ng = $ Nano gram$
\end{array}\\
$}}$$

the approximate mass of each microbe  is 20 ng (Nano gram) or $$\small{\text{$20 \cdot 10^{-9} ~g$}}$$

heureka May 7, 2015

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