Question

group 1 — problem 1
convert 5000 meters to kilometers. (1 m = 1 × 10⁻³ km)
a. 0.5 km
b. 5 km
c. 50 km
d. 500 km
notes:
1m = 0.001km 5000m × (0.001 km / 1 m) = 0.5 km

Explanation:

Step1: Recall the conversion factor

Given \( 1\ m = 1\times10^{-3}\ km \), we need to convert 5000 meters to kilometers. So we multiply the number of meters by the conversion factor.
\[
5000\ m\times(1\times10^{-3}\ \frac{km}{m})
\]

Step2: Perform the multiplication

Calculate \( 5000\times1\times10^{-3} \). We know that \( 5000 = 5\times10^{3} \), so:
\[
5\times10^{3}\times1\times10^{-3}=5\times(10^{3}\times10^{-3}) = 5\times10^{0}=5\ km
\]
Wait, there is a mistake in the note. Let's recalculate. The correct conversion: since \( 1\ km = 1000\ m \), so \( 1\ m=\frac{1}{1000}\ km = 10^{-3}\ km \). Then \( 5000\ m=5000\times10^{-3}\ km \). \( 5000\times10^{-3}=\frac{5000}{1000}=5\ km \). The note had an error in calculation (it used 0.001 as 1/1000, but 5000×0.001 is 5, not 0.5. Wait, 5000×0.001: 5000×1/1000 = 5. So the correct answer is 5 km. Let's redo the step:

Step1: Use the conversion factor

The conversion factor is \( 1\ m = 10^{-3}\ km \), so to convert meters to kilometers, we use the formula: \( \text{Kilometers}=\text{Meters}\times10^{-3} \)

Step2: Substitute the value

Substitute 5000 for Meters: \( 5000\times10^{-3} \)

Step3: Simplify the expression

\( 5000\times10^{-3}=\frac{5000}{1000}=5 \)

Answer:

b. 5 km