Question

complete the following practice problems. be sure to use the metric staircase handout as a guide. length: 1. a chemist is 350 mm in length. what is the chemist’s length in kilometers?

Explanation:

Step1: Recall metric conversions

We know that \(1\) kilometer (\(km\)) \( = 1000\) meters (\(m\)), \(1\) meter \( = 1000\) millimeters (\(mm\)). So, to convert millimeters to kilometers, we first convert millimeters to meters and then meters to kilometers.

First, convert \(350\) mm to meters. Since \(1\ m=1000\ mm\), we divide the length in millimeters by \(1000\) to get meters:
\(350\ mm=\frac{350}{1000}\ m = 0.35\ m\)

Step2: Convert meters to kilometers

Now, convert meters to kilometers. Since \(1\ km = 1000\ m\), we divide the length in meters by \(1000\) to get kilometers:
\(0.35\ m=\frac{0.35}{1000}\ km\)
Calculating \(\frac{0.35}{1000}=0.00035\ km\)

Alternatively, we can use the conversion factor directly from millimeters to kilometers. Since \(1\ km = 10^{6}\ mm\) (because \(1\ km = 1000\ m\) and \(1\ m = 1000\ mm\), so \(1\ km=1000\times1000\ mm = 10^{6}\ mm\)), we can write:
\(350\ mm=350\times\frac{1}{10^{6}}\ km\)
\(350\times10^{- 6}\ km = 3.5\times10^{-4}\ km=0.00035\ km\)

Answer:

\(0.00035\) kilometers (or \(3.5\times 10^{-4}\) kilometers)