Questions: Rank the measurements in order from smallest to largest. ≡ 1.0 × 10^-5 m ≡ 2.0 × 10^-6 m ≡ 3.0 × 10^-7 m ≡ 4.0 × 10^3 mm ≡ 1.0 m

Transcript text: Rank the measurements in order from smallest to largest. \[ \equiv 1.0 \times 10^{-5} \mathrm{~m} \] $\equiv 2.0 \times 10^{-6} \mathrm{~m}$ $\equiv 3.0 \times 10^{-7} \mathrm{~m}$ $\equiv 4.0 \times 10^{3} \mathrm{~mm}$ $\equiv 1.0 \mathrm{~m}$

Solution

Solution Steps

Step 1: Convert All Measurements to the Same Unit

Convert all measurements to meters for easy comparison.
$1.0 \times 10^{-5} \, \text{m}$ is already in meters.
$2.0 \times 10^{-6} \, \text{m}$ is already in meters.
$3.0 \times 10^{-7} \, \text{m}$ is already in meters.
$4.0 \times 10^{3} \, \text{mm} = 4.0 \times 10^{3} \times 10^{-3} \, \text{m} = 4.0 \, \text{m}$.
$1.0 \, \text{m}$ is already in meters.

Step 2: List the Measurements in Meters

$3.0 \times 10^{-7} \, \text{m}$
$2.0 \times 10^{-6} \, \text{m}$
$1.0 \times 10^{-5} \, \text{m}$
$1.0 \, \text{m}$
$4.0 \, \text{m}$

Step 3: Rank the Measurements from Smallest to Largest

$3.0 \times 10^{-7} \, \text{m}$
$2.0 \times 10^{-6} \, \text{m}$
$1.0 \times 10^{-5} \, \text{m}$
$1.0 \, \text{m}$
$4.0 \, \text{m}$

Final Answer

$\boxed{3.0 \times 10^{-7} \, \text{m}, \, 2.0 \times 10^{-6} \, \text{m}, \, 1.0 \times 10^{-5} \, \text{m}, \, 1.0 \, \text{m}, \, 4.0 \, \text{m}}$

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