Course Outline

Math Review

Measurement Using Measurements

Accuracy vs Precision Accuracy: Precision: How close a measurement is to the actual size of the object. How close a series of measurements are to each other. ACCURATE = CORRECT PRECISE = CONSISTENT

Significant Figures Indicate precision of a measurement. Recording Sig Figs: Sig figs in a measurement include the known digits plus a final estimated digit. Your answer you record can only ever be as accurate as the question cm

Significant Figures Counting Sig Figs (See Handout) As a general rule, your answer should have the same number of sig figs as the number in the question with the lease sig figs. Count all numbers EXCEPT: Leading Zeroes Sig Figs

Significant Figures Counting Sig Figs Examples Practice Sig Figs Sig Figs 3. 5,280 4 Sig Figs Sig Figs

Significant Figures Calculating With Sig Figs Multiply/Divide The # with the fewest sig figs determines the # of sig figs in the answer (13.91 g/cm 3 ) 4 Sig Figs (23.3 cm 3 ) 3 Sig Figs = g 3 Sig Figs 324 g

Significant Figures Calculating With Sig Figs (continued) Add/Subtract The # with the lowest decimal value determines the place of the last sig figs in the answer mL mL 7.85 mL 7.9 mL

Significant Figures Calculating With Sig Figs (continued) Exact Numbers The exact numbers do not limit the # of sig figs in the final answer. Example: 12 Students in a class. 1 Meter

Significant Figures Practice Problems 1. (15.30 g) ÷ (6.4 mL) g g 4 S.F 2 S.F = g/mL ~ 2.4 g/mL 2 S.F g 18.1 g

Scientific Notation 65,000 kg  6.5 X10 4 kg Converting into Scientific Notation: You take the number and move the decimal however many spots it takes until you have #.####### 1 # in front of decimal, and the rest behind. However number of spots you moved the decimal becomes the X 10 something General Rule: Large # (>>>1) Positive exponent on 10 1 or bigger Small # (<<<1) Negative exponent on or smaller

Scientific Notation 6,300,400 km Examples: = 6.3 X10 6 km 8.5 X L= 85 L

Scientific Notation Practice Problems: 1. 2,400,000 μg kg 7 X km 6.2 X 10 4 mm 2.4 X 10 6 μg 2.56 X kg km 62,000 mm

Scientific Notation Calculating with Sci. Notation (95.44 X 10 7 g) ÷ (8.1 X 10 4 mol) Type on your calculator: (5.44 X 10 ^ 7) ÷ (8.1 X 10 ^ 4) = ~ 6.7 X 10 2 g mol

Notice We can only add and subtract numbers with the same units. However, when we divide the units are divided And when we multiply the units are multiplied. Ex: 100km / 1 hour = 100km/hr ex: 5.0m * 2.0m = 10m 2

Measurement Unit Conversions

SI Prefix Conversions 1.Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places.

SI Prefix Conversions Prefix Symbol Factor mega kilo BASE UNIT deci- centi- milli- micro- nano- pico- M k d c m μ n p Move decimal to the left. Move decimal to the right.

Practice Problems 1)20cm = ___________meters 2)0.032 L = _____________mL 1)45 μm = ______________nm 1)805 dm = _____________km

Dimensional Analysis The “Factor-Label Method Units or Labels are canceled out After you cancel out all the “repeated” units, you are left with the units you use in your answer.

Dimensional Analysis The “Factor-Label Method Units or Labels are canceled out After you cancel out all the “repeated” units, you are left with the units you use in your answer.

Dimensional Analysis 1cm 3 X 4 g = 1cm 3 4 g

Cross Multiply and Divide X X 4 g = 1cm 3 4 g 4 X 1 = 4 ÷ 1 = 4

 Identify starting & ending units.  Line up conversion factors so units cancel.  Multiply all top numbers & divide by each bottom number. Cross multiply and divide  Check units & answer

Practice Problems How many milliliters are in Liters of milk?

Practice Problems How many milliliters are in Liters of milk? = 1000 so… ml/1L

Practice Problems How many milliliters are in Liters of milk? 0.946L x 1000ml/L = Use your calculator or just move the decimal 3 spots to the right. 946ml 3 Sig Figs ~ 946ml

Practice Problems A roll of wire is 1.3 M long. How many 1.5 cm long pieces can you cut from the roll? Well first we need the same units. So convert both to centimeters or both to meters.

Practice Problems A roll of wire is 1.3 M long. How many 1.5 cm long pieces can you cut from the roll?

Practice Problems A roll of wire is 1.3 M long. How many 1.5 cm long pieces can you cut from the roll? 10 2 = 100 So…. 1m = 100cm

Practice Problems A roll of wire is 1.3 M long. How many whole 1.5 cm long pieces can you cut from the roll? 1.3m X 100cm/m =130cm. 130 cm ÷ 1.5 cm/ piece = pieces ~ 86 pieces