Ch 3 Scientific Measurement Measurement Measurement A quantity

Ch. 3, Scientific Measurement

Measurement • Measurement: A quantity that has a number and a unit. Like 52 meters.

D. Scientific Notation 65, 000 kg 6. 5 × 104 kg • Converting into Sci. Notation: – Move decimal until there’s 1 digit to its left. – Any number other than 0. – Places moved = exponent. – Large # (>1) positive exponent Small # (<1) negative exponent – Only include sig figs.

D. Scientific Notation Practice Problems 7. 2, 400, 000 g 2. 4 8. 0. 00256 kg 2. 56 6 10 g -3 10 kg 7 10 -5 km 0. 00007 km 10. 6. 2 104 mm 62, 000 mm 9.

D. Scientific Notation • Calculating with Sci. Notation (5. 44 x 107 g) / (8. 1 x 104 mol) = Type of your calculator: 5. 44 EE 7 / 8. 1 EE 4 = 671. 6049383 = 670 g/mol = 6. 7 x 102 g/mol

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

Accuracy vs. Precision • *Accuracy: How close a measurement comes to the correct value. • *Precision: How close a series of measurements are to one another. – Consistency

Determining Error of a measurement • Error = Experimental Value - Accepted Value – Can be positive or negative • Percent Error = error / accepted value * 100% – or – Always positive • Example, you measured 99 cm, but it is 100 cm. 99 cm – 100 cm x 100 = 1% error 100 cm x 100

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 – (See page 24) 2. 32 cm

• 1) How many sig figs after we estimate? – 3. 2 • 2) Now how many? – 3. 13

Rules for Sig Figs • Non-Zero Numbers are always significant – Ex). 236 m has 3 sig figs. • Zeros between non-zero numbers are significant. – Ex) 7003 m and 40. 79 m each have 4 sig figs. • Leftmost zeros are not significant – Ex). 000099 m, 0. 42 m, and. 073 m each have 2 sig figs. • Rightmost zeros are significant IF they come before or after a decimal. – Ex) 9000. m, 90. 00 m, and 9. 090 m each have 4 sig figs. • Rightmost zeros with no decimal points are not significant. • Ex) 300 m has 1 sig fig. **The number of left handed people in the class is insignificant compared to the number of right handed people

C. Significant Figures Counting Sig Fig Examples 1. 23. 50 4 sig figs 2. 402 3 sig figs 3. 5, 280 3 sig figs 4. 0. 080 2 sig figs

Is a Zero a Significant Number or Not? • 504 L YES – 3 sig figs • . 06 m. L NO – 1 sig figs • 50. 0 m YES – 3 sig figs • 7, 000 km NO – 1 sig fig

C. 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)(23. 3 cm 3) = 324. 103 g 4 SF 324 g

C. Significant Figures • Calculating with Sig Figs (con’t) – Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3. 75 m. L + 4. 1 m. L 7. 85 m. L 7. 9 m. L

C. Significant Figures • Calculating with Sig Figs (con’t) – 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

• In this class, delay rounding until the very end. • 1. 8 × 2. 10 × 1. 542 Rounding: 1. 8 x 2. 10 = 3. 8 x 1. 542 = 5. 9 Round at end: 1. 8 x 2. 10 x 1. 542 = 5. 82876 = 5. 8

C. Significant Figures Practice Problems 5. (15. 30 g) ÷ (6. 4 m. L) 4 SF 2 SF = 2. 390625 g/m. L 2. 4 g/m. L 6. 18. 9 g - 0. 84 g 18. 06 g 18. 1 g 2 SF

E. SI Units Quantity Symb Base Unit Abbre ol v. Length meter m l Mass m kilogram kg Time t second s Temp T kelvin K Amount Volume n V mole liter mol L

Temperature: • Celsius and Kelvin are units of temperature that are the same, just shifted. • K = C + 273 • Water freezes at 0 C and at 273 K. • Absolute Zero = 0 K; K will never be negative. • Convert 15 C to K = 288 K • Convert 321 K to C = 48 C

E. SI Units Prefix mega- Symbol M Factor 106 kilo- k 103 BASE UNIT --- 100 deci- d 10 -1 centi- c 10 -2 milli- m 10 -3 micro- 10 -6 nano- n 10 -9 pico- p 10 -12

Different way of looking at it… • 1 km = 1000 m • 1 m = 10 dm • 1 m = 100 cm • 1 m = 1000 mm • 1 mm = 1000 um

F. Derived Units • Combination of base units. • Volume (m 3 or cm 3) – length Ø Density (kg/m 3 or g/cm 3) w mass per volume 1 cm 3 = 1 m. L 1 dm 3 = 1 L M D= V

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

Basic Algebra Review • Whatever you do to one side, you do to the other. 2 + 6 = 12 + 2 3 3

Density • An object has a volume of 825 cm 3 and a density of 13. 6 g/cm 3. Find its mass. GIVEN: WORK: V = 825 cm 3 D = 13. 6 g/cm 3 M=? M = DV M = (13. 6 g/cm 3)(825 cm 3) M = 11, 220 g 11, 200 g

Density • A liquid has a density of 0. 87 g/m. L. What volume is occupied by 25 g of the liquid? GIVEN: WORK: D = 0. 87 g/m. L V=? M = 25 g V=M D V= 25 g 0. 87 g/m. L V = 28. 7356 29 m. L

SI Prefix Conversions move right move left Prefix mega- Symbol M Factor 106 kilo- k 103 BASE UNIT --- 100 deci- d 10 -1 centi- c 10 -2 milli- m 10 -3 micro- 10 -6 nano- n 10 -9 pico- p 10 -12

SI Prefix Conversions 532 m NUMBER UNIT 0. 532 km = _______ =NUMBER UNIT

SI Unit Conversions • King __doofus can milk many newts. • k__ d c m m n • kilo, deci, centi, milli, micro, nano • What’s yours?

Dimensional Analysis • Steps: 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.

Dimensional Analysis • Lining up conversion factors: 1 in = 2. 54 cm =1 2. 54 cm 1 in = 2. 54 cm 1= 1 in

Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8. 0 cm shorter. How many inches will he be cutting off? (1 in=2. 54 cm) cm in 8. 0 cm 1 in 2. 54 cm = 3. 2 in

Dimensional Analysis • How many milliliters are in 1. 00 quart of milk? (1 L = 1. 057 qt) qt m. L 1. 00 qt 1 L 1000 m. L 1. 057 qt 1 L = 946 m. L

Dimensional Analysis • You have 1. 5 pounds of gold. Find its volume in cm 3 if the density of gold is 19. 3 g/cm 3. (1 kg = 2. 2 lbs) lb cm 3 1. 5 lb 1 kg 1000 g 1 cm 3 2. 2 lb 1 kg 19. 3 g = 35 cm 3

Dimensional Analysis • Convert 60. 0 km/hr into m/sec 60. 0 km 1000 1 hr m 1 hr 1 min 1 km 60 min 60 sec = 16. 7 m/sec

SI Prefix Conversions 1) 20 cm = 0. 2 _______ m 32 2) 0. 032 L = _______ m. L 3) 45 m = 45, 000 ____ mm 0. 0805 4) 805 dm = _______ km

Example Problems!!!

• 1. How many sig figs in: 1. 480*105. 00070 1. 000080 3. 00 E 3 • 2. Perform these calculations and come up with answers that have the correct number of sig figs: 5. 667 +. 34 5. 007 E 3 / 1. 20 4. 3 - 1. 3590 5. 309 E 3 * 3 • 3. Convert 3. 4 ug into kg. • 4. Convert 7 E 3 cm into Mm. • 5. What is the mass if a substance with a density of 4. 5 g/L has a volume of 3 L?

6. How many sig figs in: 1010 3000. 0 7. Convert 3 kg into g. Convert 34 cm into m. Convert 4 m into cm. 8. You have a 4 kg box. You measure it to be 5. 8 kg. What is the error? The % error? 9. What is the difference between accuracy and precision?

• 11. Put 5, 009, 000 into Scientific Notation • 12. Put 0. 00007890 into Scientific Notation. • 13. Put 8. 7 * 10 -4 into a regular number.

• 14. Which is the largest amount? • A. 2*102 g B. 30 kg C. 45 mg D. 190 g • 15. Convert 40 Kelvin into Celsius • 16. Convert 99 Celsius into Kelvin.