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. (-5.3 × 10^5 cm) ·[] =? km

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. (-5.3 × 10^5 cm) ·[] =? km
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. \[ \left(-5.3 \times 10^{5} \mathrm{~cm}\right) \cdot[]=? \mathrm{~km} \]
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Solution

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Solution Steps

Step 1: Recognize the Conversion Rate

To convert centimeters to kilometers, we use the conversion rate that 1 km equals 100,000 cm.

Step 2: Calculate the Conversion Factor (\(\alpha\))

Given the equation \((x \times 10^{n} \mathrm{~cm}) \cdot \alpha =? \mathrm{~km}\), we solve for \(\alpha\) by setting up the equation \(\alpha = \frac{1}{100,000}\).

Step 3: Substitute the Given Values and Solve

Substituting the given values of \(x = -5.3\) and \(n = 5\) into the equation, we calculate the converted value in kilometers. \[(-5.3 \times 10^{5} \mathrm{~cm}) \cdot \times 10^{-5} = -5.3 \mathrm{~km}\]

Final Answer:

The measurement of -5.3 \times 10^{5} cm converts to -5.3 km.

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