|2.54 cm||=||1 in|
|12 in||=||1 ft|
|5280 ft||=||1 mi|
|0.3048 m||=||1 ft|
|1 km||=||0.621 mi|
|1 furlong||=||660 ft|
|3 ft||=||1 yd|
|0.0394 in||=||1 mm|
|1 stone||=||14 lbs|
|1 lb||=||0.4536 kg|
|1 oz||=||16 drams|
|1 oz||=||28.3 g|
|16 oz||=||1 lb|
|2,000 lbs||=||1 ton|
|1 oz||=||28,350 mg|
|1 carat||=||0.2 g|
|1 cup||=||16 tablespoons|
|2 cups||=||1 pint|
|2 pints||=||1 quart|
|1 gal||=||4 quarts|
|1 gal||=||3.78 L|
|1 mL||=||1 cm3|
|1 m3||=||1000 L|
|1 cup||=||236.6 mL|
|1,000 ms||=||1 s|
|60 s||=||1 min|
|60 min||=||1 hr|
|24 hr||=||1 day|
|365 day||=||1 yr|
|14 days||=||1 fortnight|
|10 yr||=||1 decade|
|100 yr||=||1 century|
Do the following conversions using the unit factor process. Show your work for each step and cancel out units as you work. See the examples on the first page for how you should show your work! Express your answers in scientific notation when appropriate. Do all work on a separate piece of paper and number each problem clearly.
The following problems ask you to convert from one metric unit from another. Even if you know the proper metric conversion, do the calculation using the units given in the tables above. After you have finished all of the math, answer the questions below.
Some traditional units are not given in decimal form when there are whole units and parts of units. For example, weights for babies and produce are often given in this form—6 lbs 12 oz—rather than this one—6.75 lbs. Write the answers to the following conversions using this convention, which is also used for time units. For example, 2.5 hours is 2 hours 30 minutes.
1 lb 2.5 oz × --------- = 0.156 lb 16 ozSo the result is 10. 156 lb.
16 oz 0.64 lb × --------- = 10.24 oz 1 lbSo the result is 14 lb 10.2 oz.
One reason this is important is that it enables much quicker arithmetic. Try the following problems to see why. Show your work for each step of each calculation. Do not try to do it in your head!
Here are some fun trivia questions.
So far we have concentrated on cancelling units when using dimesional analysis. Units can also be combined according to the rules of algebra. For example, 12x multiplied by 9/4x equals 27 because the x cancels out and 12/4 × 9 is 27. If the problem had been 2x multiplied by 5x then the answer is 10x2. The x variables combine to be written together as x2 instead of x · x. Here are some examples with actual units:
Area Density 5 cm × 2 cm = 10 cm2 5 g Volume ------ = 1.67 g/cm3 1 m × 2 m × 3 m = 6 m3 3 cm3
The general idea is that if a unit does not cancel out during the calculation, it is still there at the end. Combine like terms and pay attention to whether the unit is in the numerator (on top) or in the denominator (on the bottom).
Here are two examples of problems solved by using combined units.
Convert 42 ft2 to m2 42 ft2 42 ft·ft 0.3048 m 0.3048 m ------ = --------- x ---------- x ---------- = 3.9 m2 1 1 1 ft 1 ft Enter this into your calculator as 42 × 0.3048 × 0.3048 = 3.90192768
Find the volume in mL of 63 g of gold, which has a density of 19.3 g/mL 63 g 1 mL ------ x --------- = 3.26 mL 1 19.3 g Enter this into your calculator as 63 ÷ 19.3 = 3.264248705
Areas and volumes are examples of combined units, for the most part. An acre is an example of a unit of area which is not a combined unit. A gallon is similarly a unit of volume which is not a combined unit. Square feet (ft2) are really (feet) times (feet) because that’s how area is calculated. Similarly, a cubic meter (m3) can be imagined as a cubic space one meter on a side. For area units you must convert with two conversion factors. For volume, use three conversion factors.
Common units of speed are miles per hour (mi/hr), kilometers per hour (km/hr), meters per second (m/s), centimeters per second (cm/s), kilometers per second (km/s), and miles per second (mi/s). Show work as always. There is an example of this type of calculation in the introduction.
Density is often taught using the formula D = m/V. Since students frequently make mistakes using this formula a better way to proceed is to use dimensional analysis, as in the example shown above. Some useful data: the density of aluminum is 2.70 g/mL; the density of lead is 11.3 g/cm3; the density of water is 1 g/mL.