Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out
Get this document free

Dimensional Analysis Factor – Label Method Unit Factor Method (DOC)

VIEWS: 298 PAGES: 2

									Dimensional Analysis/Factor Label Method/Unit Factor Method
Dimensional analysis is a simple and straightforward method for converting from a particular unit to one that is related to it by an equivalent relationship. It is based on the idea that multiplication by one (The Multiplicative Identity Property of Algebra) does not change the value of an expression. Dimensional analysis takes a relationship between units in an equation (equivalence statement) and expresses that equivalent relationship as a fraction (conversion factor or unit factor). This unit factor is a factor in which the numerator and denominator are expressed in different units but represent the same or equivalent amounts. For example 2.54 cm = 1 in is an equivalence statement. Two conversion factors, which may be obtained from this equivalence, are

2.54 cm 1 in

and

1 in 2.54 cm

To apply the concept of dimensional analysis to problem solving, let the units lead you in the direction you need to go to obtain the desired quantity. General Steps for Doing Conversions by Dimensional Analysis: 1. To convert from one unit to another, use the equivalence statement that relates the two units. The conversion factor needed is a ratio of the two parts of the equivalence statement. 2. Choose the appropriate conversion factor by looking at the direction of the required change. (Make sure the unwanted units cancel and that you are left with the units you want in the result.) 3. Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. 4. Check to see that you have the correct number of significant figures. 5. Ask whether your answer makes sense.

Example: 5.00 km = __________ miles Necessary equivalence statements: 5280 ft = 1 mile 12 in = 1 ft 2.54 cm = 1 in 100 cm = 1 m 1000 m = 1 km 5.00 km 1000 m 1 km 100 cm 1m 1 in 2.54 cm 1 ft 12 in 1 mile 5280 ft = 3.11 miles

Dimensional Analysis/Factor Label Method/Unit Factor Method
Dimensional analysis is a simple and straightforward method for converting from a particular unit to one that is related to it by an equivalent relationship. It is based on the idea that multiplication by one (The Multiplicative Identity Property of Algebra) does not change the value of an expression. Dimensional analysis takes a relationship between units in an equation (equivalence statement) and expresses that equivalent relationship as a fraction (conversion factor or unit factor). This unit factor is a factor in which the numerator and denominator are expressed in different units but represent the same or equivalent amounts. For example 2.54 cm = 1 in is an equivalence statement. Two conversion factors, which may be obtained from this equivalence, are

2.54 cm 1 in

and

1 in 2.54 cm

To apply the concept of dimensional analysis to problem solving, let the units lead you in the direction you need to go to obtain the desired quantity. General Steps for Doing Conversions by Dimensional Analysis: 6. To convert from one unit to another, use the equivalence statement that relates the two units. The conversion factor needed is a ratio of the two parts of the equivalence statement. 7. Choose the appropriate conversion factor by looking at the direction of the required change. (Make sure the unwanted units cancel and that you are left with the units you want in the result.) 8. Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. 9. Check to see that you have the correct number of significant figures. 10. Ask whether your answer makes sense.

Example: 5.00 km = __________ miles Necessary equivalence statements: 5280 ft = 1 mile 12 in = 1 ft 2.54 cm = 1 in 100 cm = 1 m 1000 m = 1 km 5.00 km 1000 m 1 km 100 cm 1m 1 in 2.54 cm 1 ft 12 in 1 mile 5280 ft = 3.11 miles


								
To top