Questions: A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. (0.050 cm) . =? km × 10 μ .

A student sets up the following equation to convert a measurement.
(The ? stands for a number the student is going to calculate.)
Fill in the missing part of this equation.
(0.050 cm) . =? km × 10 μ .

Transcript text: A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. $(0.050 \mathrm{~cm})$. $\square$ $=? \mathrm{~km}$ $\square$ $\times 10$ $\mu$ $\square$ $\square$ $\square$ $\cdot$

Solution

Solution Steps

To solve the problem of converting a measurement from centimeters to kilometers, we need to understand the conversion factors between these units. The conversion from centimeters to kilometers involves converting centimeters to meters first, and then meters to kilometers. Specifically, 1 cm is equal to 0.01 meters, and 1 meter is equal to 0.001 kilometers. Therefore, to convert from centimeters to kilometers, we multiply the number of centimeters by 0.01 and then by 0.001.

Step 1: Convert Centimeters to Meters

To convert the measurement from centimeters to meters, we use the conversion factor $ 1 \, \text{cm} = 0.01 \, \text{m} $. Thus, we have: \[ 0.050 \, \text{cm} \times 0.01 = 0.0005 \, \text{m} \]

Step 2: Convert Meters to Kilometers

Next, we convert the result from meters to kilometers using the conversion factor $ 1 \, \text{m} = 0.001 \, \text{km} $: \[ 0.0005 \, \text{m} \times 0.001 = 5 \times 10^{-7} \, \text{km} \]