Question

unit conversion problems
solve using dimensional analysis. make sure you show how the units are canceled.
warning: when using a calculator, put everything you have on your denominator between parentheses so that nothing goes back up to the numerator!
units of mass: 1 kg = 1000 g, 1 lbs = 453.59 g
units of distance: 1 m = 100 cm = 1000 mm, 1 km = 1,000 m, 1 mi = 1.609 km, 1 in = 2.54 cm
units of volume: 1 cm³ = 1 ml, 1 m³ = 1,000,000 cm³, 1 l = 1000 ml, 1 gallon = 3.8 l
units of time: 1 year = 365.25 days, 1 day = 24 h, 1 h = 60 min, 1 min = 60 s
examples:

1. one - unit conversion: how many cubic centimeters (cm³) are there in one gallon?

1 gallon / 1 gallon 3.8 l / 1 gallon 1000 ml / 1 l 1 cm³ / 1 ml = (1 3.8 1000 1) / (1 1 1) = 3800 cm³
leave empty for one - unit conversion

1. two - unit conversion: the speed limit for cars is 70 miles per hour (mph) on the highway. convert to meter per second (m/s):

70 mi / 1 h 1.609 km / 1 mi 1000 m / 1 km 1 h / 60 min 1 min / 60 s = (70 1.609 1000 1 1) / (1 1 1 60 60) = 31 m/s
practice, practice, practice:

1. convert 12 meters (m) to inches (in):
2. convert 568 cm to meters (m):

Explanation:

Step1: Identify the conversion factor

We know that 1 in = 2.54 cm and 1 m=100 cm. So 1 m = $\frac{100}{2.54}$ in.

Step2: Convert 12 meters to inches

We have 12 m. Using the conversion factor, we multiply 12 by $\frac{100}{2.54}$. So the number of inches is $12\times\frac{100}{2.54}=\frac{1200}{2.54}\approx472.44$ in.

Step3: Convert 568 cm to meters

Since 1 m = 100 cm, to convert 568 cm to m, we divide 568 by 100. So $568\div100 = 5.68$ m.

Answer:

1. Approximately 472.44 in
2. 5.68 m