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Chapter 3 Measurement Accuracy vs Precision Percent Error Significant Figures Scientific Notation Temperature Conversions Dimensional Analysis Conversion.

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Presentation on theme: "Chapter 3 Measurement Accuracy vs Precision Percent Error Significant Figures Scientific Notation Temperature Conversions Dimensional Analysis Conversion."— Presentation transcript:

1 Chapter 3 Measurement Accuracy vs Precision Percent Error Significant Figures Scientific Notation Temperature Conversions Dimensional Analysis Conversion Factors SI Conversions

2 Number vs. Quantity Quantity - number + unit UNITS MATTER!!

3 A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

4 A. Accuracy vs. Precision

5 B. Percent Error Indicates accuracy of a measurement your value given value

6 B. Percent Error A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.94 %

7 C. Significant Figures Indicate precision of a measurement. Recording Sig Figs – Sig figs in a measurement include the known digits plus a final estimated digit 2.31 cm

8 C. Significant Figures Counting Sig Figs – Digits from 1-9 are always significant – Zeros between two other sig figs are always significant – One or more additional zeros to the right of both the decimal place and another sig digit are significant – Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,

9 , C. Significant Figures Counting Sig Fig Examples , sig figs 3 sig figs 2 sig figs

10 C. Significant Figures Calculating with Sig Figs – Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer (13.91g/cm 3 )(23.3cm 3 ) = g 324 g 4 SF3 SF

11 C. Significant Figures Calculating with Sig Figs (cont) – Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer 3.75 mL mL 7.85 mL 7.9 mL 3.75 mL mL 7.85 mL

12 C. Significant Figures Calculating with Sig Figs (cont) – Exact Numbers do not limit the # of sig figs in the answer Counting numbers: 12 students Exact conversions: 1 m = 100 cm 1 in any conversion: 1 in = 2.54 cm

13 C. Significant Figures 5. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL 18.1 g g g g 4 SF2 SF 2.4 g/mL 2 SF

14 D. Scientific Notation A way to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to a power (exponent) Number of carbon atoms in the Hope diamond 460,000,000,000,000,000,000,000 atoms 4.6 x atoms coefficient exponent

15 D. Scientific Notation Converting into Sci. Notation: – Move decimal until theres 1 digit to its left. Places moved = exponent – Large # (>1) positive exponent Small # (<1) negative exponent – Only include sig figs – all of them! 65,000 kg 6.5 × 10 4 kg

16 D. Scientific Notation 7. 2,400,000 g kg km mm Practice Problems g kg km 62,000 mm

17 D. Scientific Notation Calculating with Sci. Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE = = 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator:

18 D. Scientific Notation 11. (4 x 10 2 cm) x (1 x 10 8 cm) 12. (2.1 x kg) x (3.3 x 10 2 kg) 13. (6.25 x 10 2 ) ÷ (5.5 x 10 8 ) 14. (8.15 x 10 4 ) ÷ (4.39 x 10 1 ) 15. (6.02 x ) ÷ (1.201 x 10 1 ) Practice Problems cm kg x x x 10 22

19 CH. 3 - MEASUREMENT Temperature Conversions

20 A. Temperature Temperature – measure of the average KE of the particles in a sample of matter

21 Temperature Convert these temperatures: 1)25 o C = ______________K 2)-15 o F = ______________ K 3)315K = ______________ o C 4)288K = ______________ o F

22 Measurement Dimensional Analysis

23 A. Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

24 B. Dimensional Analysis Dimensional Analysis – A tool often used in science for converting units within a measurement system Conversion Factor – A numerical factor by which a quantity expressed in one system of units may be converted to another system

25 B. Dimensional Analysis The Factor-Label Method – Units, or labels are canceled, or factored out

26 B. Dimensional Analysis Steps to solving problems: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

27 C. Conversion Factors F ractions 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.

28 How many minutes are in 2.5 hours? Conversion factor cancel 2.5 hr 1 x xx x 60 min 1 hr = 150 min

29 C. Conversion Factors Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers 1 L 1000 mL 1 hr 60 min 1000 m 1 km 1000 mL 1 L =

30 D. SI Prefix Conversions 1.Memorize the following chart. (next slide) 2.Find the conversion factor(s). 3.Insert the conversion factor(s) to get to the correct units. 4.When converting to or from a base unit, there will only be one step. To convert to or from any other units, there will be two steps.

31 A. SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro nano-n10 -9 kilo-k10 3 BASE UNIT giga-G10 9 deka-da10 1 hecto-h10 2 tera-T10 12 move left move right

32 = A. SI Prefix Conversions NUMBER UNIT NUMBER UNIT 532 m = _______ km 0.532

33 D. SI Prefix Conversions 1 T(base) = (base) = (base) 1 G(base) = (base) = 10 9 (base) 1 M(base) = (base) = 10 6 (base) 1 k(base) = (base) = 10 3 (base) 1 h(base) = 100 (base) = 10 2 (base) 1 da(base) = 10 (base) 1 (base) = 1 (base) 10 d(base) = 1 (base) 100 c(base) = 1 (base) 1000 m (base) = 1 (base) 10 6 µ(base) = µ(base) = 1(base) 10 9 n(base) = n(base) = 1(base) micro

34 D. SI Prefix Conversions a. cm to m b. m to µm c. ns to s d. kg to g 1 m 100 cm 1 m 10 6 µm 1 s 10 9 ns 1 kg 1000 g

35 D. SI Prefix Conversions 1)20 cm = ______________ m 2) L = ______________ mL 3) 45 m = ______________ m

36 D. SI Prefix Conversions 4) 805 Tb = ______________ b 805 Tb b 1 Tb Terabytes bytes = 805 x bytes = 8.05 x bytes 8.05 x 10 14

37 D. SI Prefix Conversions 5) 400. g = ______________ kg 6) 57 Mm = ______________ nm

38 E. Dimensional Analysis Practice 1.You have $7.25 in your pocket in quarters. How many quarters do you have?

39 E. Dimensional Analysis Practice 2. How many seconds are in 1.4 days? Plan: days hr min seconds

40 E. Dimensional Analysis Practice 3. How many milliliters are in 1.00 quart of milk?

41 E. Dimensional Analysis Practice 4.You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3.

42 5. Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? E. Dimensional Analysis Practice

43 6. Milton football needs 550 cm for a 1 st down. How many yards is this? E. Dimensional Analysis Practice

44 7. A piece of wire is 1.3 m long. How many 1.5- cm pieces can be cut from this wire? E. Dimensional Analysis Practice

45 8. How many liters of water would fill a container that measures 75.0 in 3 ?


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