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Chapter 9: Problem 100

Convert to an appropriate metric unit so that the numerical expression in the given measure does not contain any zeros. \(0.0002 \mathrm{~km}\)

Short Answer

Expert verified
\(0.0002 \mathrm{~km}\) is equivalent to \(0.2 \mathrm{~m}\).

Step by step solution

01

Understand metric units

The first step is to understand the various metric units and how they relate to each other. From larger to smaller, some of the most commonly used units of length in the metric system are kilometers (km), meters (m), centimeters (cm) and millimeters (mm) with the following relationships: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm. Given that our original measurement is in kilometers, we need to convert it to one of the smaller units.
02

Convert km to other units and check for zeros

Next, convert the measurement from kilometers to the other units, and check for the presence of zeros in the numerical expression. Starting with meters, we know that 1 km = 1000m, so \(0.0002 \mathrm{~km}\) is \(0.0002 \times 1000 = 0.2 \mathrm{~m}\). Next, convert from meters to centimeters. Given that 1 m = 100 cm, so \(0.2 \mathrm{~m}\) is \(0.2 \times 100 = 20 \mathrm{~cm}\). As the numerical expression still contains zeros, consider a smaller unit, millimeters. From centimeters to millimeters, where 1 cm = 10 mm, so \(20 \mathrm{~cm}\) gives \(20 \times 10 = 200 \mathrm{~mm}\).
03

Choose the correct unit

In the previous step, we have converted the given measurement into three different units. According to the exercise, we have to select the unit that does not contain any zeros in the numerical expression. Observing the converted values, meters (0.2 m) is the only unit that does not have zero in its numerical expression. Hence, \(0.0002 \mathrm{~km}\) will be \(0.2 \mathrm{~m}\).

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