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The highlights are:

• Conversion factors

• Standard dimensional analysis

• Dimensional analysis with exponential units

• Conversion factors

• Standard dimensional analysis

• Dimensional analysis with exponential units

1.
Dimensional Analysis

In which you will learn about:

•Conversion factors

•Standard dimensional analysis

•Dimensional analysis with exponential units

In which you will learn about:

•Conversion factors

•Standard dimensional analysis

•Dimensional analysis with exponential units

2.
Dimensional Analysis

• Imagine math class (don’t panic)

• Imagine multiplying two fractions

• Imagine the numerator of one fraction

matches the denominator of the second (3/7 x

2/3)

• The numerator and denominator cancel!

• In dimensional analysis, we use this idea to

cancel UNITS of measurements.

• Imagine math class (don’t panic)

• Imagine multiplying two fractions

• Imagine the numerator of one fraction

matches the denominator of the second (3/7 x

2/3)

• The numerator and denominator cancel!

• In dimensional analysis, we use this idea to

cancel UNITS of measurements.

3.
Equalities

State the same measurement in two different units

10.0 in.

25.4 cm

State the same measurement in two different units

10.0 in.

25.4 cm

4.
Conversion Factors

Fractions in which the numerator and denominator are

EQUAL quantities expressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

Fractions in which the numerator and denominator are

EQUAL quantities expressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

5.
How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 60 min = 150 min

1 hr

cancel

By using dimensional analysis / factor-label method, the UNITS

ensure that you have the conversion right side up, and the

UNITS are calculated as well as the numbers!

Conversion factor

2.5 hr x 60 min = 150 min

1 hr

cancel

By using dimensional analysis / factor-label method, the UNITS

ensure that you have the conversion right side up, and the

UNITS are calculated as well as the numbers!

6.
Sample Problem

• You have $7.25 in your pocket in quarters.

How many quarters do you have?

7.25 dollars X 4 quarters = 29 quarters

1 dollar

• You have $7.25 in your pocket in quarters.

How many quarters do you have?

7.25 dollars X 4 quarters = 29 quarters

1 dollar

7.
Learning Check

A rattlesnake is 2.44 m long. How long is the

snake in cm?

a) 2440 cm

b) 244 cm

c) 24.4 cm

A rattlesnake is 2.44 m long. How long is the

snake in cm?

a) 2440 cm

b) 244 cm

c) 24.4 cm

8.
Solution

A rattlesnake is 2.44 m long. How long is the

snake in cm?

b) 244 cm

2.44 m x 100 cm = 244 cm

1m

A rattlesnake is 2.44 m long. How long is the

snake in cm?

b) 244 cm

2.44 m x 100 cm = 244 cm

1m

9.
Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

60 min x 60 s = 1.2 x 105 s

1.4 days x 24 hr x

1 hr 1 min

1 day

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

60 min x 60 s = 1.2 x 105 s

1.4 days x 24 hr x

1 hr 1 min

1 day

10.
Wait a minute!

What is wrong with the following setup?

1.4 day x 1 day x 60 min x 60 sec

24 hr 1 hr 1 min

What is wrong with the following setup?

1.4 day x 1 day x 60 min x 60 sec

24 hr 1 hr 1 min

11.
English and Metric Conversions

• If you know ONE conversion for each type of

measurement, you can convert anything!

• I will provide these equalities, but you must be

able to use them:

– Mass: 454 grams = 1 pound

– Length: 2.54 cm = 1 inch

– Volume: 0.946 L = 1 quart

• If you know ONE conversion for each type of

measurement, you can convert anything!

• I will provide these equalities, but you must be

able to use them:

– Mass: 454 grams = 1 pound

– Length: 2.54 cm = 1 inch

– Volume: 0.946 L = 1 quart

12.
Steps to Problem Solving

Read problem

Identify data

Make a unit plan from the initial unit to the desired

unit (good practice at beginning, not necessary as you

get comfortable with this)

Select conversion factors

Change initial unit to desired unit

Cancel units and check

Do math on calculator

Give an answer using significant figures

Read problem

Identify data

Make a unit plan from the initial unit to the desired

unit (good practice at beginning, not necessary as you

get comfortable with this)

Select conversion factors

Change initial unit to desired unit

Cancel units and check

Do math on calculator

Give an answer using significant figures

13.
Dealing with Two Units

If your pace on a treadmill is 65 meters per minute,

how many seconds will it take for you to walk a

distance of 8450 feet?

HINT: Always start with the simplest label.

You’re looking for seconds, so you can’t start there.

65 m/min has two labels so that’s not very simple.

Best STARTING place is 8450 feet!

If your pace on a treadmill is 65 meters per minute,

how many seconds will it take for you to walk a

distance of 8450 feet?

HINT: Always start with the simplest label.

You’re looking for seconds, so you can’t start there.

65 m/min has two labels so that’s not very simple.

Best STARTING place is 8450 feet!

14.
What about Square and Cubic units?

• Use the conversion factors you already know,

but when you square or cube the unit, don’t

forget to cube the number also!

• Best way: Square or cube the ENTIRE

conversion factor

• Example: Convert 4.3 cm3 to mm3

4.3 cm3

( )

10 mm 4.3 cm3 103 mm3

3

=

1 cm 13 cm3

= 4300 mm3

• Use the conversion factors you already know,

but when you square or cube the unit, don’t

forget to cube the number also!

• Best way: Square or cube the ENTIRE

conversion factor

• Example: Convert 4.3 cm3 to mm3

4.3 cm3

( )

10 mm 4.3 cm3 103 mm3

3

=

1 cm 13 cm3

= 4300 mm3

15.
Learning Check

• A Nalgene water

bottle holds 1000 cm3

of dihydrogen

monoxide (DHMO).

How many cubic

decimeters is that?

• A Nalgene water

bottle holds 1000 cm3

of dihydrogen

monoxide (DHMO).

How many cubic

decimeters is that?

16.
Solution

1000 cm3 1 dm 3

( )

10 cm

= 1 dm3

So, a dm3 is the same as a Liter !

A cm3 is the same as a milliliter.

1000 cm3 1 dm 3

( )

10 cm

= 1 dm3

So, a dm3 is the same as a Liter !

A cm3 is the same as a milliliter.

17.
How do I round multiple step

problems with the correct sig figs?

• If the problem has only one “type” of math

(adding/subtracting OR multiplying/dividing),

round at the end of the problem

– Dimensional analysis is all M/D! Round at the end.

• If the problem has more than one type, you must

follow the order of operations, round after each

type is complete.

– A good example is percent error. Round using adding

rules after 0-E, then finish the calculation and round

again using multiplying rules.

problems with the correct sig figs?

• If the problem has only one “type” of math

(adding/subtracting OR multiplying/dividing),

round at the end of the problem

– Dimensional analysis is all M/D! Round at the end.

• If the problem has more than one type, you must

follow the order of operations, round after each

type is complete.

– A good example is percent error. Round using adding

rules after 0-E, then finish the calculation and round

again using multiplying rules.

18.
Speaking of Sig Figs…

• Exact conversion factors, such as 100 cm in 1

m, do NOT count toward the number of sig

figs!

• Numbers that are part of a mathematical

formula, such as x100 in percent error, do

NOT count toward the number of sig figs!

• Exact conversion factors, such as 100 cm in 1

m, do NOT count toward the number of sig

figs!

• Numbers that are part of a mathematical

formula, such as x100 in percent error, do

NOT count toward the number of sig figs!