Factor Labeling or DA

Problem Solving: The easy way!!!

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Factor Label Method Objectives

• How to solve a problems just using units• How to solve 1 dimension -

1 conversion problems• How to solve 1 dimension –

2 conversion problems• How to solve multidimensional –

multiconversion problems

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Factor Label Method

• No one method is best for solving every type of problem

• We Use Dimensional Analysis!!!

• Use the units (dimensions) that are part of the measurement to help solve (analyze ) the problem

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How to solve a problems just using units

A. You must write the following steps inorder to get full credit.

1. Write what you know.2. Write what you don’t know.3. Write a plan on how to get from the known to the unknown.4. Write the conversion(s) you are going to use.

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How to solve a problems just using units

A. You must write the following steps inorder to get full credit.

5. Complete the table a. Draw a table based on the below:

1 column for known1 column for each conversion1 column for the unknownEvery table has 2 rows

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How to solve a problems just using units

A. You must write the following steps inorder to get full credit.

5. Complete the table

Known_Unit

(Given)

Unknown_Units

Conversion (Answer)Unknown_Unit

(Answer)Known_Units

Conversion (Given)

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How to solve a problems just using units

6. How do you know what goes on top in the conversion column?

The units you start with go on the bottom. The units you end with go on the top.Known_Unit

(Given)

Unknown_Units

Conversion (Answer)Unknown_Unit

(Answer)Known_Units

Conversion (Given)

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How to solve a problems just using units

7. The first column is always what you start with.

8. The last column is always what you need to end with.Known_Unit

(Given)

Unknown_Units

Conversion (Answer)Unknown_Unit

(Answer)Known_Units

Conversion (Given)

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How to solve a problems just using units

9. Notice the red units drop out, Z*X/Z = X

and you are left with the answer.

Known_Unit

(Given)

Unknown_Units

Conversion (Answer)Unknown_Unit

(Answer)Known_Units

Conversion (Given)

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How to solve a problems just using units

10. IE: How many inches are in X feet?Known: X feet?: inchesPlan: feet inchesConversion: 1_ft = 12_in

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How to solve a problems just using units

10: How many inches are in X feet?Known: X feet?: inchesPlan: feet inchesConversion: 1_ft = 12_in

X feet 12 inches inches

1 feet

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How to solve a problems just using units

10: How many inches are in X feet?The vertical lines mean multiplication The horizontal lines mean divisionSince its either multiplication or division there is no order of operations!

X feet 12 inches (X * 12) inches

1 feet

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Sig Fig (Significant Figure) Rules

1.Any number 1-9 is significant1.1234 has 4 sig figs2.12340000 has 4 sig figs3.0123400 has 4 sig figs

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Sig Fig (Significant Figure) Rules

2. Zeros are the problem1. Zero is not a number but a construct or

idea!2. Zeros sandwiched between numbers

1. 101 3 sig figs2. 0101 3 sig figs3. 010100 3 sig figs4. 1.01 3 sig figs5. 0.101 3 sig figs

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Sig Fig (Significant Figure) Rules

2. Zeros are the problem1. Zero is not a number but a construct or

idea!2. Zeros sandwiched between numbers

1. 101 3 sig figs2. 0101 3 sig figs3. 010100 3 sig figs4. 1.01 3 sig figs5. 0.101 3 sig figs

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Sig Fig (Significant Figure) Rules

2. Zeros are the problem3. Decimal Points mess zeros

3. Any zero after a number & before and/or after a decimal point is significant1. 1000. 4 sig figs2. 100.0 4 sig figs3. 0.1000 4 sig figs

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Sig Fig (Significant Figure) Rules

3. Sig figs in calculations1. Conversion Factors or constants have unlimited sig figs so we ignore them2. If its addition or subtraction

1. Not really sig figs – least number of digits to the right of the decimal place wins1. 15.2 + .002 = 15.22. 15.2 – 7 = 8

3. If its multiplication or division least number of sig figs wins1. 2.0 * .33333333 = .67 Notice rounding2. 5.00/2.5000 = 2.00

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Sig Fig (Significant Figure) Rules

3. Sig figs in calculations4. It goes by last operation performed

1. So if last operation is + or –1. Least digits to the right of decimal

2. So if last operation is * or / 1. Least number of sig figs2. THIS IS WHAT WE USE THE MOST!

5. Rounding1. Find last sig fig – look next door

1. If less than 5, drop everything to right including it2. If equal to or greater than five round up 1

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Sig Fig (Significant Figure) Rules

3. Sig figs in calculations5. Rounding

1. Find last sig fig – look next door1. If less than 5, drop everything to right including it2. If equal to or greater than five round up 1

2. If need three sig figs1. 2.333 becomes 2.332. 1.009 becomes 1.013. 15.9996 becomes 16.0

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How to solve 1 dimension - 1 conversion problems

B. How many grams are in 750 centigrams?

Known = 750 centigramsUnknown = grams

Plan: cg g

Conversion Factor(s): 100 cg = 1 g

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How to solve 1 dimension - 1 conversion problems

B. How many grams are in 750 centigrams?Known = 750 centigramsUnknown = grams

Plan: cg g

Conversion Factor(s): 100 cg = 1 g

750 cg | 1 g | 7.5_g__

| 100 cg |

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How to solve 1 dimension - 2 conversion problems

B. How many tons are in 4536 kilograms?Known = 4536 kilogramsUnknown = tons

Plan: kg pounds tons

Conversion Factor(s): .4536_kg = 1_lb, 2000_lb = 1_ton

4536_kg 1_lb 1_ton 5.000_ton

.4536_kg 2000_lb

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1 dimension – multiconversionsC. How many seconds are in 5

days?

Unknown = seconds

Known = 5 days

Conversion Factor(s): 1 day = 24 hours 1 hour = 60 min

1 min = 60 sec 5 days | 24 hrs | 60 min | 60 sec = 432,000_sec = 4.32 X

105 sec

| 1 day | 1 hr | 1 min 1

Solve the problem:

Plan: day hour min sec

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How to solve 2 dimension - 2 conversion problems

D. How many km/l are in 12_mi/gal?

1. 2 dimensions – mi to km & gal to litersKnown = 12_mi/galUnknown = km/L

Plan: mi/gal km/L

Conversion Factor(s): 1_mi = 1.609_km & 1 gal = 3.785_L

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How to solve 2 dimension - 2 conversion problems

D. How many km/L are in 12_mi/gal?What is the sig fig answer? 5.1_km/L

12_mi 1.609_km 1_gal 5.101_km

gal 1_mi 3.785_L L

Deriving Units• Find the line, square and cube on page 1 of

C2 DA Packet

• Notice the line = 1_m, square = 1_m2 and the cube = 1_m3

• Let 100_cm = 1_m

• Now put 100_cm on each edge of square and solve for how many cm2 in 1_m2

• What is 100 cm * 100 cm?

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Deriving Units• Find the line, square and cube on page 1 of

C2 DA Packet

• Notice the line = 1_m, square = 1_m2 and the cube = 1_m3

• Let 100_cm = 1_m

• Now put 100_cm on each edge of square and solve for how many cm3 in 1_m3

• What is 100 cm * 100 cm * 100 cm?

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Final Thoughts

• That last technique works for anything unit that starts with a length.

• You must use the conversions on the sheet

• Your homework is the C2 DA Packet• Its due the next class meeting

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