1

Scientific Measurement

2

Quantitative vs. Qualitative

Quantitative measurement:

Number + units

“This person has a

temperature of 102.3 F.”

Qualitative measurement:

Descriptive

“This person feels feverish.”

3

Precise: how close a group of

measurements are.

Accurate: how close to the true

value a measurement is.

accurate

& precise

precise

onlyneither

4

Precision vs. Accuracy ?

A student measured her

height to be 153, 155 and

156 cm.

Her true height is 168 cm.

Precise and/or accurate?

(Instruments are calibrated

to give accurate measurements)

5

Error

Student measures temperature

of boiling water to be 103.2oC.

The true value is 100.0oC.

Error = measured - accepted

= 103.2oC – 100.0oC

= 3.2oC

6

3.2oC

100oC= x 100

Percent Error

Percent error =error

acceptedx 100

= 3.2%

7

Percent Error: Try It

A Quality Control technician

measures that there are

only 1.92 L of soda in a

bottle that should contain

2.00 L. What is the % error

in filling the bottle?

8

Scientific Notation

Avogadro’s Number:

602,200,000,000,000,000,000,000

6.022 x 1023

Mass of H atom

0.00000000000000000000000166 g

1.66 x 10-24 g

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Scientific Notation

N. x 10m

6.02 x 1023

coefficient exponent

10

Scientific Notation

1.Start with number in decimal form.

2.Count number of places to move

decimal point to get one digit to the

left of the decimal point.

•shift decimal left exp. increases

•shift decimal right exp. decreases

0.00083 = 8.3 x 10-4

11

Scientific Notation: Try It !

Express in proper scientific notation:

2001.

0.00345

40230000.

34.5 x 105

34.5 x 10-5

0.029 x 10-6

12

Scientific Notation

Can you go backwards?

Express as decimal numbers.

3.3 x 10-3

6.2 x 104

13

Using Scientific Notation

Multiplication (& division):

•multiply (divide) coefficients and

add (or subtract) exponents

(8.0 x 10-2) x (7.0 x 105) =

= 56 x 103

= 5.6 x 104

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Using Scientific Notation

Try it !

(8.0 x 10-2) (7.0 x 105) = ?

x

y

x divided by y:

xy x/y per

Note:

15

Addition & subtraction:•convert to same exponents, then

just add (or subtract) coefficients

(3.42 x 10-5) - (2.5 x 10-6) =

(3.42 x 10-5) - (0.25 x 10-5) =

= 3.17 x 10-5

Using Scientific Notation

Using a Scientific

Calculator

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(3.42 x 10-5) - (2.5 x 10-6) =

3.42E-5 - 2.5E-6 enter

Do not use the 10x button!

17

Scientific Notation Try It!

(6.2 x 10-3) x (1.5 x 101)

(8.8 x 106) (2.2 x 10-1)

(6.7 x 10-2) + (3.0 x 10-3)

(7.32 x 104) – (6.10 x 103)

Try with & without scientific calc.

Significant Figures

18

If I asked you to measure the

width of this room, how many

digits would you write down?

30 ft

32 ft

32.4 ft

32.43 ft

32.437 ft

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--read the scale

--estimate one more digit

--always use units

Significant Figures:

0.6m

0.61m

0.607m. . . . . . . . .

. . . . . . . . .

Significant Figures

20

--read the scale

--estimate one more digit

--always use units

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Reading Sig Fig: Rules

All non-zeros are significant.

1.234 ft

Zeros between non-zero

numbers are significant.

40,501 ft

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Significant Figures

Zeros to the left of the first non-zero number are not significant.

0.00349 ft

Zeros to right of the last non-zero number are significant if there is a decimal point.

0.09030 ft

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Significant Figures

300 ft 1 sig fig

300. ft 3 sig figs

How would you show 2 sig figs?

Need scientific notation:

3. x 102 ft 1 sig fig

3.0 x 102 ft 2 sig figs

3.00 x 102 ft 3 sig figs

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“Exact” Numbers(unlimited sig figs)

Counting: for example, 8 people

25

Many conversion factors:

12 inches = 1 foot

12.000… in = 1.0000… ft

“Exact” Numbers(unlimited sig figs)

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How Many Sig Figs ?

123 m

0.123 m

40506 m

9.800 x 104 m

0.07080 m

98000 m

6 bottles

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Rounding

32.6 to 2 sig figs is 33.

314.721 to 4 sig figs is ?

0.001775 to 2 sig figs is ?

9792 to 2 sig figs is ?

If digit after the last sig fig is >5,

increase the last sig fig by 1.

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Sig Figs in Calculations

Addition & Subtraction: Sig figs of

answer determined by number with

fewest digits to right of decimal.

12.52

+ 349.0

361.52

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Honors:

(3.467 x 10-3) + (6.7 x 10-2) = ?

3.467 + 6.7 = ?

Addition & Subtraction: Try It!

30

Multiplication & Division: Sig figs of

answer determined by number

with the least number of sig figs.

2.4526 8.3 = ?

= 0.295493976

= 0.30

Sig Figs in Calculations

31

(8.2 x 10-3) x (7.25 x 108) = ?

(6.234 x 10-5) (4.3 x 10-2) = ?

Multiplication / Division: Try It!

32

Sig Figs in Calculations

With your backpack on,

your mass is 72.1 kg.

Your mass is 65.42 kg.

What is the mass of your

backpack?

33

Sig Figs in Calculations

How many fluid ounces are there

per glass if a 32 oz. soda bottle is

divided evenly among 7 glasses?

34

Metric (SI) Units

Add 9 in + 1 yd 2 ft 4 in38

316

Add 16.54 cm + 1.0160 m

compared to:

Which is easier?

35

Metric SystemRegents Table D

Quantity Units

Length Meter

Volume Cubic Meter, Liter

Mass Gram, Kilogram

Temp Kelvin, Celsius

Time Second

Energy Joule

36

Prefixes (Regents Table C)

Prefix Symbol Factor

kilo k 103

deci d 10-1

centi c 10-2

milli m 10-3

micro m 10-6

e.g. 1 cm = 10-2 m = 0.01 m

37

Write an equality for the following units:

1 mm = ? m

4.3 cg = ? g

3 kg = ? g

6.9 ms = ? s

Prefixes (Regents Table C)

38

Metric Length

Unit Examples

kilometer (km) ~5/8 mile

meter (m) ~ yard

centimeter(cm) width of button

millimeter (mm) thickness of dime

micrometer (mm) diameter of cell

39

Metric VolumeVolume related to length:

(length3 = V)Unit Examples

Cubic centimeter Cube of sugar

(cm3 = cc)

Liter (L) Quart of milk

Milliliter (mL) 20 drops water

Note: 1cm3 = 1mL

40

Metric Mass

Unit Examples Kilogram (kg) Small textbook

Gram (g) Paperclip

Milligram (mg) Ten grains of salt

1 mL = 1 cm3 = 1g H2O

Density

41

Reading assignment handout.

Sink or float?

42

Question ????

Which is heavier: a pound of lead

or a pound of feathers ?

vs. ?

43

Density

Density = massvolume

Density of a substance is

independent of the mass

and volume.

Density of 2 kg of Pb is 11.4 g/cm3

Density of 9 kg of Pb is 11.4 g/cm3

44

Density

Density scale is defined by water.

Recall:

1 mL = 1 cm3 = 1g H2O

Thus DH2O = 1.00g

cm3

45

Density

Density in g/cm3 at 25oC

Au 19.3 H2O 0.997

Hg 13.5 H2O 1.00 (4oC)

Pb 11.4 Ice 0.917 (0oC)

Fe 7.87 Gasoline 0.66-0.69

Al 2.70 Wood 0.11-1.33

Bone 1.7-2.0 Air 0. 00119

46

Density

A plastic ball with a volume of 19.7

cm3 has a mass of 15.8 g.

Would this ball sink or float in a

container of gasoline?

(Density of gasoline is 0.68 g/cm3.)

47

Temperature

Recall: temperature is

a measure of the average kinetic

energy of atoms & molecules.

Atoms & molecules

are always in motion.

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Temperature

Is there a temperature where

motion stops ?

Yes! absolute zero

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Temperature Scales

Celsius Kelvin

No motion-273 0

373Water boils 100

273Water freezes 0

(Size of

degree is

the same)

50

Temperature Scales

Converting: Celsius Kelvin

K = oC + 273

Regents Table T

51

Temperature Scales

K = oC + 273Convert:

•25oC to K

•150K to oC

What is the difference between

the B.P. and F.P. of water in oC & in K?

52

Heat

Heat, a form of energy, flows

between two objects if they are at

different temperatures.

Hot Cold

53

Heat

Heat (energy) is not

temperature (a measurement).

Which burns more: spoonful of

boiling water or pot of boiling water ?

54

Warm-up

55

Which is bigger?

102 or 103

10-2 or 10-3

Note: 102 = 1 x 102

Warm-up

56

Express in scientific notation:

0.000745 6,283,000,000

Do the following calculations:

6.2E-4 / 8.1E-3 =

7.1E-2 + 6.0E-3 =

Note: 6.2 x 10-4 = 6.2E-4

Warm-up

57

What are sig figs?

How many sig figs in:

0.090300 m?

42 sandwiches?

Warm-up

58

Do the calculation, express in proper

scientific notation and sig figs:

5.41cm + .27568 cm =

2.772E-2 cm / 8.1E3 cm =

Honors:

5.417E-2 cm + 2.7E-3 cm =

Warm-up

59

Do the calculation, express in proper

scientific notation and sig figs:

4.61 – 0.3472 =

6.77E-2 * 3.17841E3 =

How many meters are in 6.4 mm?

Warm-up

60

•How many grams are in 7.9 ng?

•What is the relationship between

volume in cm3, volume in mL,

and mass?