Question

multi - step conversions using dimensional analysis
sometimes you dont have a direct conversion factor to get from your given units to your desired units. you can use two or more conversion factors at once to accomplish your task most efficiently.
example: you must convert 345 ounces to kilograms. but you have no conversion between the two.

1. find two conversions that together will take you step - wise to your desired units. in this case:

1 pound = 16 ounces and 1 kilogram = 2.2046 pounds

1. write your starting number with units. in this case 345 oz
2. arrange and multiply the conversion factors so that the first cancels your original units, and the second cancels the intermediate units and leaves you with your desired units.

345 oz x 1 lb / 16 oz x 1 kg / 2.2046 lb = 9.78 kg
use two or more conversions factors together to make the following conversions

1. convert 725 milliliters to gallons
2. convert 2.5 miles to meters
3. convert 6,834 centimeters to miles
4. convert 825 ounces to liters

challenge question:
our track star can leap 96 cm high. how far is this in miles? show your conversion as one long chained dimensional analysis problem.

Explanation:

Step1: Identify conversion factors

1 gallon = 3785.41 milliliters, 1 mile = 1609.34 meters, 1 mile = 160934 centimeters, 1 liter = 33.814 ounces, 1 mile = 160934 centimeters

Step2: Convert 725 milliliters to gallons

$725\ ml\times\frac{1\ gal}{3785.41\ ml}\approx 0.192\ gal$

Step3: Convert 2.5 miles to meters

$2.5\ mi\times\frac{1609.34\ m}{1\ mi}=4023.35\ m$

Step4: Convert 6834 centimeters to miles

$6834\ cm\times\frac{1\ mi}{160934\ cm}\approx 0.0425\ mi$

Step5: Convert 825 ounces to liters

$825\ oz\times\frac{1\ L}{33.814\ oz}\approx 24.4\ L$

Step6: Convert 96 cm to miles for challenge question

$96\ cm\times\frac{1\ m}{100\ cm}\times\frac{1\ km}{1000\ m}\times\frac{1\ mi}{1.60934\ km}\approx 5.97\times 10^{-4}\ mi$

Answer:

1. 0.192 gal
2. 4023.35 m
3. 0.0425 mi
4. 24.4 L

Challenge Question: $5.97\times 10^{-4}$ mi