Questions: A penny is found to have a length of 2.17 × 10^-2 meters. Using unit analysis, show what the length of the penny is in millimeters.

Transcript text: A penny is found to have a length of $\mathbf{2 . 1 7} \times \mathbf{1 0}^{-2}$ meters. Using unit analysis, show what the length of the penny is in millimeters.

Solution

Solution Steps

Step 1: Identify the given value and its unit

The given length of the penny is $2.17 \times 10^{-2}$ meters.

Step 2: Determine the conversion factor

To convert meters to millimeters, we use the conversion factor $1 \text{ meter} = 1000 \text{ millimeters}$.

Step 3: Set up the unit conversion

Multiply the given length by the conversion factor to convert meters to millimeters: \[ 2.17 \times 10^{-2} \text{ meters} \times \frac{1000 \text{ millimeters}}{1 \text{ meter}} \]

Step 4: Perform the multiplication

\[ 2.17 \times 10^{-2} \times 1000 = 2.17 \times 10^{3-2} = 2.17 \times 10^{1} = 21.7 \]