One way of assuring yourself that you are getting the CORRECT answer

Dimensional Analysis is the mathematical process of converting a given

measurement to another unit.

If you can multiply fractions, you can do Dimensional Analysis.

Use dimensional analysis when converting a given result from one system of units to another.1) To convert from one unit to another, use the

equivalence statement that relates the two units.2) Choose the appropriate conversion factor by

looking at the direction of the required change (make sure the unwanted units cancel).

3) Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units.

4) Check that you have the correct number of sig figs.

5) Ask, does my answer make sense?

A conversion factor is an multiplier for converting a one set of units

into another.

12 in = 1 ft 1 in = 2.54 cm 2.2 lbs = 1 kg 1 cm = 10-2 m

Typically we display conversion factors as fractions.

OROR OROR OROR OROROROR =

100 cm = 1 m

It helps to create a “Plan of Attack” with conversion factors to reach a desired unit.

To do this the given unit (the unit you start with) is in the denominator and your

desired unit (the unit you want) is in the numerator.

Example… Convert ft → in

1ft x 12 in = 12 in

1ft

Example #1

1 ft 12 in and

12 in 1 ft

A golfer putted a golf ball 6.8 ft across a green. How many

inches does this represent?

To convert from one unit to another, use the equivalence

statement that relates the two units.

1 ft = 12 in

The two conversion factors are:

Derive the appropriate conversion factor by looking at the direction of the required change (to cancel the unwanted units).

Notice – start with what was given Notice - the units in the numerator of the first term are in the denominator of the

second term. This will always be the case.

Example #1A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?

6.8 ft12 in

1 ft

Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units.

Correct sig figs? Does my answer make sense?

Example #1A golfer putted a golf ball 6.8 ft across a green. How many inches does this

represent?

6.8 ft12 in

1 ft

82 in

More practice … Convert 15.5 ft → in

Plan: ft → in

Conversion Factor:

Given measurement = 15.5 ft

15.5 ft x 12 in = 186 in

1 ft

You try: Convert 23 in → cm

Remember there are 2.54 cm in an inch Answer: 58.42 -> 58 cm (2 sig figs)

Sometimes you will need multiple conversion factors to reach a

desired unit.

Example… Convert yds → m

Plan: yds → ft → in → cm → m

Example… Convert 75.0 yds → m75.0 yds x 3 ft x 12 in x 2.54 cm x 1 m = 6,858 -> 6,860 m (3 sig figs)

1 yd 1 ft 1 in 100 cm

Example #2An iron sample has a mass of 4.50 lb. What is the mass of this sample in

grams?

(1 kg = 2.2046 lbs; 1 kg = 1000 g)

Steps:

•Begin with what was given (4.5 lbs)

•Select appropriate conversion factor(s) so units cross off4.50 lbs

1 kg 2.2046 lbs

1000 g

1 kg 3= 2.04 10 g

Example #3A car is traveling at a rate of 65 miles per hour. How fast is the car traveling in km per sec? (1.61km = 1 mile)Note we will solve it two ways – either way is fineHere we began by converting hours to secondsWe used lines instead of parenthesis to help keep terms in the numerator and denominators separate.

Note – Here we began by converting miles to km

=

65 miles

1 hour

1 hour

60 min

1 min

60 sec

1.61 km

1 mile

= 0.029km/sec

65 miles

1 hour

1.61 km

1 mile

1 hour

60 min

1 min

60 sec

0.029km/sec

Concept CheckWhat data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation.Sample Answer:Distance between New York and Los Angeles: 2500 milesAverage gas mileage: 25 miles per gallonAverage cost of gasoline: $3.25 per gallon

1 gal $3.252500 mi = $325

25 mi 1 gal