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Course Outline. Math Review. Measurement Using Measurements. Accuracy:. How close a measurement is to the actual size of the object. Precision:. How close a series of measurements are to each other . ACCURATE = CORRECT PRECISE = CONSISTENT. Accuracy vs Precision.

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## Course Outline

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**Measurement**Using Measurements**Accuracy:**How close a measurement is to the actual size of the object. Precision: How close a series of measurements are to each other. ACCURATE = CORRECT PRECISE = CONSISTENT Accuracy vs Precision**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. 2.35 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--0.0025 2 Sig Figs**Significant Figures**Counting Sig Figs Examples Practice 1. 23.50 4 Sig Figs 402 2. 3 Sig Figs 3. 5,280 4 Sig Figs 4. 0.080 2 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/cm3) (23.3 cm3) 324.103g = 4 Sig Figs 3 Sig Figs 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. 3.75 mL + 4.1 mL 7.9 mL 7.85 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. 12.0000000000 1.0000000000**Significant Figures**Practice Problems 1. (15.30 g) ÷ (6.4 mL) = 2.390625 g/mL 2 S.F 2 S.F 4 S.F ~ 2.4 g/mL 2. 18.9 g - 0.84 g 18.1 g 18.06 g**Scientific Notation**65,000 kg 6.5 X104 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 10something General Rule: Large # (>>>1) Positive exponent on 101 or bigger Small # (<<<1) Negative exponent on 10-1 or smaller**Scientific Notation**Examples: 6,300,400 km = 6.3 X106 km 3 2 1 4 6 5 0 0 8.5 X 10-7 L = 85 L 0 0 0 0 0 1 7 6 4 5 3 2**Scientific Notation**Practice Problems: 1. 2,400,000 μg 2.4 X 106μg 2. 0.00256 kg 2.56 X 10-3 kg 3. 7 X 10-5 km 0.00007 km 4. 6.2 X 104 mm 62,000 mm**Scientific Notation**Calculating with Sci. Notation (95.44 X 107 g) ÷ (8.1 X 104 mol) Type on your calculator: 4) ^ (5.44 X 10 ^ 7) (8.1 X 10 ÷ = 671.6049383 ~ 6.7 X 102 g mol**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 = 10m2 Notice**Find the difference between the exponents of the two**prefixes. • 2. Move the decimal that many places. SI Prefix Conversions**Prefix Symbol Factor**M 106 mega kilo BASE UNIT deci- centi- milli- micro- nano- pico- k 103 --- 100 d 10-1 c 10-2 m 10-3 μ 10-6 n 10-9 SI Prefix Conversions p 10-12 Move decimal to the left. Move decimal to the right.**20cm = ___________meters**0.032 L = _____________mL 45μm = ______________nm 805 dm = _____________km 0.2 32 45000 0.0805 Practice Problems**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**1cm3 X 4 g =**4 g 1cm3 Dimensional Analysis**X X 4 g =**4 g • 1cm3 1cm3 Cross Multiply and Divide 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**How many milliliters are in 0.946 Liters of milk?**Practice Problems**How many milliliters are in 0.946 Liters of milk?**10-3 = 1000 so….. 1000 ml/1L Practice Problems**How many milliliters are in 0.946 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? 102 = 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 = 86.666666666667 pieces ~ 86 pieces Practice Problems

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