# Factor Labeling or DA Problem Solving: The easy way!!!

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Factor Labeling or DA Problem Solving: The easy way!!!

1/17/2014 10:52 PMC2 Factor Labeling or DA2 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

1/17/2014 10:52 PMC2 Factor Labeling or DA3 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

1/17/2014 10:52 PMC2 Factor Labeling or DA4 How to solve a problems just using units A. You must write the following steps in order to get full credit. 1. Write what you know. 2. Write what you dont 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.

1/17/2014 10:52 PMC2 Factor Labeling or DA5 How to solve a problems just using units A. You must write the following steps in order to get full credit. 5. Complete the table a. Draw a table based on the below: 1 column for known 1 column for each conversion 1 column for the unknown Every table has 2 rows

1/17/2014 10:52 PMC2 Factor Labeling or DA6 How to solve a problems just using units A. You must write the following steps in order to get full credit. 5. Complete the table Known_Unit (Given) Unknown_Units Conversion (Answer) Unknown_Unit (Answer) Known_Units Conversion (Given)

1/17/2014 10:52 PMC2 Factor Labeling or DA7 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)

1/17/2014 10:52 PMC2 Factor Labeling or DA8 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)

1/17/2014 10:52 PMC2 Factor Labeling or DA9 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)

1/17/2014 10:52 PMC2 Factor Labeling or DA10 How to solve a problems just using units 10. IE: How many inches are in X feet? Known: X feet ?: inches Plan: feet inches Conversion: 1_ft = 12_in

1/17/2014 10:52 PMC2 Factor Labeling or DA11 How to solve a problems just using units 10: How many inches are in X feet? Known: X feet ?: inches Plan: feet inches Conversion: 1_ft = 12_in X feet12 inchesinches 1 feet

1/17/2014 10:52 PMC2 Factor Labeling or DA12 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 division Since its either multiplication or division there is no order of operations! X feet12 inches(X * 12) inches 1 feet

1/17/2014 10:52 PMC2 Factor Labeling or DA13 Sig Fig (Significant Figure) Rules 1. Any number 1-9 is significant 1. 1234 has 4 sig figs 2. 12340000 has 4 sig figs 3. 0123400 has 4 sig figs

1/17/2014 10:52 PMC2 Factor Labeling or DA14 Sig Fig (Significant Figure) Rules 2. Zeros are the problem 1. Zero is not a number but a construct or idea! 2. Zeros sandwiched between numbers 1.101 3 sig figs 2.01013 sig figs 3.010100 3 sig figs 4.1.013 sig figs 5.0.1013 sig figs

1/17/2014 10:52 PMC2 Factor Labeling or DA15 Sig Fig (Significant Figure) Rules 2. Zeros are the problem 1. Zero is not a number but a construct or idea! 2. Zeros sandwiched between numbers 1.101 3 sig figs 2.01013 sig figs 3.010100 3 sig figs 4.1.013 sig figs 5.0.1013 sig figs

1/17/2014 10:52 PMC2 Factor Labeling or DA16 Sig Fig (Significant Figure) Rules 2. Zeros are the problem 3. Decimal Points mess zeros 3.Any zero after a number & before and/or after a decimal point is significant 1.1000.4 sig figs 2.100.04 sig figs 3.0.10004 sig figs

1/17/2014 10:52 PMC2 Factor Labeling or DA17 Sig Fig (Significant Figure) Rules 3. Sig figs in calculations 1. Conversion Factors or constants have unlimited sig figs so we ignore them 2. If its addition or subtraction 1.Not really sig figs – least number of digits to the right of the decimal place wins 1.15.2 +.002 = 15.2 2.15.2 – 7= 8 3. If its multiplication or division least number of sig figs wins 1.2.0 *.33333333=.67 Notice rounding 2.5.00/2.5000= 2.00

1/17/2014 10:52 PMC2 Factor Labeling or DA18 Sig Fig (Significant Figure) Rules 3. Sig figs in calculations 4. 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 figs 2.THIS IS WHAT WE USE THE MOST! 5. Rounding 1.Find last sig fig – look next door 1.If less than 5, drop everything to right including it 2.If equal to or greater than five round up 1

1/17/2014 10:52 PMC2 Factor Labeling or DA19 Sig Fig (Significant Figure) Rules 3. Sig figs in calculations 5. Rounding 1.Find last sig fig – look next door 1.If less than 5, drop everything to right including it 2.If equal to or greater than five round up 1 2.If need three sig figs 1.2.333 becomes 2.33 2.1.009 becomes 1.01 3.15.9996 becomes 16.0

1/17/2014 10:52 PMC2 Factor Labeling or DA20 How to solve 1 dimension - 1 conversion problems B. How many grams are in 750 centigrams? Known = 750 centigrams Unknown = grams Plan: cg g Conversion Factor(s): 100 cg = 1 g

1/17/2014 10:52 PMC2 Factor Labeling or DA21 How to solve 1 dimension - 1 conversion problems B. How many grams are in 750 centigrams? Known = 750 centigrams Unknown = grams Plan: cg g Conversion Factor(s): 100 cg = 1 g 750 cg | 1 g | 7.5_g__ | 100 cg |

1/17/2014 10:52 PMC2 Factor Labeling or DA22 How to solve 1 dimension - 2 conversion problems B. How many tons are in 4536 kilograms? Known = 4536 kilograms Unknown = tons Plan: kg pounds tons Conversion Factor(s):.4536_kg = 1_lb, 2000_lb = 1_ton 4536_kg1_lb1_ton5.000_ton.4536_kg2000_lb

1/17/2014 10:52 PMC2 Factor Labeling or DA23 1 dimension – multiconversions C. 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 10 5 sec | 1 day | 1 hr | 1 min 1 Solve the problem: Plan: day hour min sec

1/17/2014 10:52 PMC2 Factor Labeling or DA24 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 liters Known = 12_mi/gal Unknown = km/L Plan: mi/gal km/L Conversion Factor(s): 1_mi = 1.609_km & 1 gal = 3.785_L

1/17/2014 10:52 PMC2 Factor Labeling or DA25 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_mi1.609_km1_gal5.101_km gal1_mi3.785_L L

Deriving Units Find the line, square and cube on page 1 of C2 DA Packet Notice the line = 1_m, square = 1_m 2 and the cube = 1_m 3 Let 100_cm = 1_m Now put 100_cm on each edge of square and solve for how many cm 2 in 1_m 2 What is 100 cm * 100 cm? 1/17/2014 10:52 PMC2 Factor Labeling or DA26

Deriving Units Find the line, square and cube on page 1 of C2 DA Packet Notice the line = 1_m, square = 1_m 2 and the cube = 1_m 3 Let 100_cm = 1_m Now put 100_cm on each edge of square and solve for how many cm 3 in 1_m 3 What is 100 cm * 100 cm * 100 cm? 1/17/2014 10:52 PMC2 Factor Labeling or DA27

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 1/17/2014 10:52 PMC2 Factor Labeling or DA28

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