Question

Dimensional Analysis problems Solve the following problem using dimensional analysis. Remember that you must show your work to earn credit. 1. Convert the 6.0 feet, a recommendation for social distancing, to nanometers (nm). Given: • 6.0 feet Unknown: • The equivalent distance in nanometers (nm)

Answer 1

To convert 6.0 feet to nanometers using dimensional analysis, you can use the conversion factors: 1 foot = 30.48 cm, 1 cm = 0.01 m, and 1 m = 10^9 nm. Multiplying the given measurement by these conversion factors, you can find that 6.0 feet is equivalent to 1.8288 * 10^9 nm.

Step-by-step explanation:

To convert 6.0 feet to nanometers (nm) using dimensional analysis, we can use the conversion factor that 1 foot is equal to 30.48 centimeters (cm). Then, we can convert centimeters to meters by dividing by 100 (since there are 100 centimeters in a meter). Finally, we can convert meters to nanometers by multiplying by 10^9 (since there are 10^9 nanometers in a meter).

Here are the steps:

1. Given: 6.0 feet
2. Conversion factor: 1 foot = 30.48 cm
3. Conversion factor: 1 cm = 0.01 m
4. Conversion factor: 1 m = 10^9 nm
5. Step 1: Multiply 6.0 feet by the first conversion factor: 6.0 feet * 30.48 cm/foot = 182.88 cm
6. Step 2: Multiply 182.88 cm by the second conversion factor: 182.88 cm * 0.01 m/cm = 1.8288 m
7. Step 3: Multiply 1.8288 m by the third conversion factor: 1.8288 m * 10^9 nm/m = 1.8288 * 10^9 nm