Conversion Factors and Unit Cancellation

A physical quantity must include: Number + Unit + Unit

Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot = 12 inches

Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1

Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1 12 inches 1 foot = 1

Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors”

Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors” 3 feet 3 feet 12 inches 12 inches 1 foot 1 foot = 36 inches ( ( ) ) ( ( ) )

Dimensional Analysis A mathematical way to convert one unit to another. This works for metric units and non-metric (English) units. This works by taking the unit you are given and multiplying it by a conversion factor. CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

Example 1: Convert 3m to cm Given Conversion Factor For meters to cancel out, meters in the conversion factor must be on the opposite side of the fraction (fence). CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 3m 100 cm 1m Multiply every number on top of the fence and divide by the bottom.

Example 2: Convert 1516 g to kg conversion factor CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula g 1 kg 1000 g

Whiteboard Problem 1 Convert 1200 cm to m. CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

Example 4: Convert 7200mm to km 7200 mm =.0072 km CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 10 mm 1 cm 1 km 100,000 cm

Non-Metric (English) Unit Conversions Common Conversion Factors –5280 ft = 1 mile –12 in = 1 ft –1 mile = 1600 m –1 in = 2.54 cm –3 ft = 1 yard CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. English to Metric conversion factors

Example 4: Convert 2 miles to ft CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 2 mi 5280 ft 1 mi

Whiteboard Problem 4 Convert 5 ft to cm CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

Example 5: Convert 5 ft to cm CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 5 ft 12 in 1 ft 2.54 cm 1 in

How many cm are in 1.32 meters? applicable conversion factors: equality: or X cm = 1.32 m= 1 m = 100 cm ______1 m 100 cm We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. ______ 1 m 100 cm () ______ 1 m 100 cm 132 cm (or 0.01 m = 1 cm)

How many meters is 8.72 cm? applicable conversion factors: equality: or X m = 8.72 cm= 1 m = 100 cm ______1 m 100 cm Again, the units must cancel. ______ 1 m 100 cm () ______ m 1 m 100 cm

How many feet is inches? applicable conversion factors: equality: or X ft = in= 1 ft = 12 in ______1 ft 12 in Again, the units must cancel. () ____ 3.28 ft 1 ft 12 in ______ 1 ft 12 in

How many kilometers is 15,000 decimeters? X km = 15,000 dm= 1.5 km () ____ 1,000 m 1 km 10 dm 1 m () ______

How many seconds is 4.38 days? = 1 h 60 min24 h 1 d1 min 60 s ____ ()() () _____ X s = 4.38 d 378,432 s3.78 x 10 5 s If we are accounting for significant figures, we would change this to…

The steps to follow Now we are ready to solve problems using the factor label method. The steps involved are: 1.Write down the desired quantity/units 2.Equate the desired quantity to given quantity 3.Determine what conversion factors you can use (both universal and question specific) 4.Multiply given quantity by the appropriate conversion factors to eliminate units you don’t want and leave units you do want 5.Complete the math

Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = miles) First write down the desired quantity # km

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Next, equate desired quantity to the given quantity # km= 47 mi Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Now we have to choose a conversion factor # km= 47 mi Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) What conversion factors are possible? # km= 47 mi 1 km mi 1 km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Pick the one that will allow you to cancel out miles # km= 47 mi 1 km mi 1 km Factor label example

Pick the one that will allow you to cancel out miles Q - How many kilometers are in 47 miles? (note: 1 km = miles) # km= 47 mi 1 km mi 1 km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Multiply given quantity by chosen conversion factor # km= 47 mi 1 km mi 1 km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Multiply given quantity by chosen conversion factor # km= 47 mi x 1 km mi Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Cross out common factors # km= 47 mi x 1 km mi Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Cross out common factors # km= 47 x 1 km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Are the units now correct? # km= 47 x 1 km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Yes. Both sides have km as units. # km= 47 x 1 km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Yes. Both sides have km as units. # km# km = 47 x 1 km # km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) Now finish the math. # km= 47 x 1 km = 75.7 km Factor label example

Q - How many kilometers are in 47 miles? (note: 1 km = miles) The final answer is 75.7 km # km= 47 x 1 km = 75.7 km Factor label example

Summary The previous problem was not that hard In other words, you probably could have done it faster using a different method However, for harder problems the factor label method is easiest

Real Life Chemistry Keys Real Life Chemistry

Simple Math with Conversion Factors

Measured dimensions of a rectangle: Find area of rectangle. A = L. W = (9.70 cm)(4.25 cm) length (L) = 9.70 cm width (W) = 4.25 cm L W = Example Problem 41.2cm 2. cm

Convert 41.2 cm 2 to m cm 1 m () ______ X m 2 = 41.2 cm 2 X m 2 = 41.2 cm. cm Recall that…41.2 cm 2 = 41.2 cm. cm 100 cm 1 m () ______ X m 2 = 41.2 cm 2 =0.412 m 2 =0.412 cm. m WRONG! () ______ 100 cm 1 m = m 2 () ______ 100 cm 1 m 2 = m 2

Convert 41.2 cm 2 to mm 2. X mm 2 = 41.2 cm 2 X mm 2 = 41.2 cm. cm Recall that…41.2 cm 2 = 41.2 cm. cm 1 cm 10 mm () _____ =4,120 mm 2 = 1 cm 10 mm () _____ 4,120 mm 2 1 cm 10 mm 2 () _____

Measured dimensions of a rectangular solid: Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L. W. H = (15.2 cm)(3.7 cm)(8.6 cm) =480cm 3

Convert to m 3. X m 3 = 480 cm 3 = m cm 1 m 3 () _____ X m 3 = 480 cm 3 = X m 3 = cm 1 m () _____ 100 cm 1 m () _____ 100 cm 1 m () _____ = or cm. cm. cm 1 m cm ( ) _________ x m 3 or 3 2 cm

Measured dimensions of a rectangular solid: Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L. W. H = (0.152 m)(0.037 m)(0.086 m) = m m m m Convert to m 3...

Convert to mm 3.

By what factor do mm and cm differ? 10 By what factor do mm 2 and cm 2 differ? 100 By what factor do mm 3 and cm 3 differ? 1,000 1 cm = 10 mm (1 cm) 2 = (10 mm) 2 1 cm 2 = 100 mm 2 (1 cm) 3 = (10 mm) 3 1 cm 3 = 1000 mm 3

Conversion Factors Keys Conversion Factors