Ch 3 Scientific Measurement Measurement A quantity that
- Slides: 56
Ch. 3, Scientific Measurement
Measurement • : A quantity that has a and a. Like 52 meters.
Scientific Notation • Writing long numbers as smaller ones to a power of ten. • = 1. 4 x 106 = 1. 4 E 6 • . 00056 = = 5. 6 E-4 • 15, 093, 000 = 1. 5093 x 107 =
Accuracy vs. Precision • * : How close a measurement comes to the value. • * : How close a series of measurements are to.
Determining Error of a measurement = Experimental Value - Accepted Value – Can be positive or • Percent Error = error / accepted value * 100% – or • – Always • Example, you measured 99 cm, but it is 100 cm.
• : The digits in a measurement that are known plus one that is not known. – Filled 43. 1 m. L
Rules for Sig Figs • Non-Zero Numbers are always significant – Ex). 236 m has sig figs. • Zeros between non-zero numbers are significant. – Ex) 7003 m and 40. 79 m each have sig figs. • Leftmost zeros are not significant – Ex). 000099 m, 0. 42 m, and. 073 m each have sig figs. • Rightmost zeros are significant if they come before or after a period. – Ex) 9000. m, 90. 00 m, and 9. 090 m each have sig figs.
Rules for Sig Figs • Rightmost zeros with no decimal points are no significant. • Ex) 300 m has sig fig. • Exactly defined quantities have an number of sig figs. • Seen most when converting between measurements. • 60 min = 1 hour, 100 cm = 1 m each have an unlimited number of sig figs.
Is a Zero a Significant Number or Not? • • 504 L. 06 m. L 50. 0 m 7, 000 km
Sig Figs in Calculations: • Calculations be more precise than the precise measurement. • Addition or subtraction - Round the final answer to the same number of decimal places as the measurement with the number of decimal places. – the last “shared column”. • 13. 4 m + 5. 254 m = 18. 7 m
Sig Figs in Calculations: • Multiplication or Division - The final answer should have the number of sig figs as the measurement that has the number of sig figs. • 2. 4526 m x 8. 4 m = 21 m
• In this class, delay rounding until the very end. • (3. 449 L + 6. 57 L) * 8. 779 L / 5. 2 L = 17 L
International System of Units • How much of something you have is given by Units. Like centimeters, kilometers, etc. • is the standard measurement system for science.
• • * The five SI units used most by chemists are: Distance = (m) Mass = kilogram (kg) Temperature = (K) Time = second (s) Volume = liter (L) Amount = (mol).
• Prefixes can be used in front of units for powers of 10.
• = how much “stuff” is in something. How much matter is in something. • = the pull on something by gravity. • If I go to the moon, which changes and which stays constant? changes, stays the same.
Temperature: • Celsius and Kelvin are units of temperature that are the , just shifted. • K = C + 273 • Water freezes at 0 C and at K. • Absolute Zero = 0 K; a K value will never be negative.
*Energy • * - The ability to do work or produce heat. • (J) is the SI unit of energy. • • 1 J =. 239 cal (cal) is another unit of energy.
Conversions Convert 7 mm to m. Convert 12. 4 Mm to cm.
• Convert 7 km/ms to m/s • An experiment asks students to measure 1. 50 g of Cu wire. All we have is a 40. 0 g spool of Cu. How many students can do the experiment?
*Density • * = mass / volume • What is the density of 2 g of salt in a volume of 4 L? • What is the density in g/L of 5 kg of salt in a volume of 6 m. L?
If silver has a density of 10. 5 g/L, what is the volume of a silver coin that has a mass of 14 g?
• Density as temperature increases. • D=m/v • As T increases, V • Therefore, density decreases. .
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 ng 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 mass and weight? 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.
More from Chp 3 • I. Using Measurements
A. Accuracy vs. Precision • - how close a measurement is to the accepted value • - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT
C. Significant Figures • Indicate precision of a measurement. • Recording Sig Figs – Sig figs in a measurement include the digits plus a final – (See page 24) 2. 32 cm _ digit
• 1) How many sig figs after we estimate? • 2) Now how many?
C. Significant Figures • Counting Sig Figs – Count all numbers EXCEPT: • ________zeros -- 0. 0025 • Trailing zeros _________ a decimal point -- 2, 500
C. Significant Figures Counting Sig Fig Examples 1. 23. 50 sig figs 2. 402 sig figs 3. 5, 280 sig figs 4. 0. 080 sig figs
C. Significant Figures • Calculating with Sig Figs – Multiply/Divide - The # with the sig figs determines the # of sig figs in the answer. (13. 91 g/cm 3)(23. 3 cm 3) = 324. 103 g
C. Significant Figures • Calculating with Sig Figs (con’t) – Add/Subtract - The # with the 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
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
C. Significant Figures Practice Problems 5. (15. 30 g) ÷ (6. 4 m. L) = 2. 390625 g/m. L 6. 18. 9 g - 0. 84 g 18. 06 g
D. Scientific Notation 65, 000 kg 6. 5 × 104 kg • Converting into Sci. Notation: – Move decimal until there’s Places moved = – Large # (>1) Small # (<1) – Only include sig figs. digit to its left. . exponent
D. Scientific Notation Practice Problems 7. 2, 400, 000 g 8. 0. 00256 kg 9. 7 10 -5 km 10. 6. 2 104 mm
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
E. SI Units Quantity Symb Base Unit Abbre ol v. l Length meter Mass m kilogram Time t second s kelvin K Temp Amount n mole
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
F. Derived Units • Combination of base units. • Ø (m 3 or cm 31) – length cm 3 = 1 m. L 1 dm 3 = 1 L (kg/m 3 or g/cm 3) w mass per volume M D= V
Problem-Solving Steps 1. _ 2. Plan 3. Compute 4. _
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= D= M=? M= M= M=
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= V=? M= V= V= V=
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 Unit Conversions • King __doofus can milk many newts. • k__ d c m m n • kilo, deci, • What’s yours? , milli, ,
SI Prefix Conversions 532 m NUMBER UNIT = _______ km NUMBER UNIT =
SI Prefix Conversions 1) 20 cm = _______ m 2) 0. 032 L = _______ m. L 3) 45 m = ____ mm 4) 805 dm = _______ km
Dimensional Analysis • Steps: 1. Identify starting & units. 2. Line up conversion factors so units 3. Multiply all 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 • How many milliliters are in 1. 00 quart of milk? (1 L = 1. 057 qt) qt m. L 1. 00 qt
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 1. 5 lb cm 3
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
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