Ch 3 Scientific Measurement Measurement A quantity that

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Ch. 3, Scientific Measurement

Ch. 3, Scientific Measurement

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

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

Scientific Notation • Writing long numbers as smaller ones to a power of ten.

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.

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

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

• : 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

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.

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.

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. •

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

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

• 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

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

• • * 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.

• Prefixes can be used in front of units for powers of 10.

 • = how much “stuff” is in something. How much matter is in

• = 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

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)

*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.

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

• 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

*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

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 •

• Density as temperature increases. • D=m/v • As T increases, V • Therefore, density decreases. .

Example Problems!!!

Example Problems!!!

 • 1. How many sig figs in: 1. 480*105. 00070 1. 000080 3.

• 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

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.

• 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

• 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

More from Chp 3 • I. Using Measurements

A. Accuracy vs. Precision • - how close a measurement is to the accepted

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 –

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

• 1) How many sig figs after we estimate? • 2) Now how many?

C. Significant Figures • Counting Sig Figs – Count all numbers EXCEPT: • ________zeros

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

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

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 #

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

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)

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

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

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) /

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

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

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

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. _

Problem-Solving Steps 1. _ 2. Plan 3. Compute 4. _

Density • An object has a volume of 825 cm 3 and a density

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

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-

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

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 532 m NUMBER UNIT = _______ km NUMBER UNIT =

SI Prefix Conversions 1) 20 cm = _______ m 2) 0. 032 L =

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

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

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

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

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

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