Scientific Measurements

Accuracy vs. Precision

Significant Figures

Scientific Notation

SI Metric units

Density

Dimensional Analysis

2

How good are the measurements?

Scientists use two word to describe how good the measurements are

Accuracy- how close the measurement is to the actual value

Precision- how well can the measurement be repeated

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

the accepted true value

• Precision - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT

4

Differences Accuracy can be true of an individual

measurement or the average of several Precision requires several

measurements before anything can be said about it

examples

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Let’s use a golf anaolgy

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Accurate? No

Precise? Yes

7

Accurate? Yes

Precise? Yes

8

Precise? No

Accurate? Maybe?

9

Accurate? Yes

Precise? We cant say!

10

In terms of measurement A room is exactly 10.3 m

wide Three students measure

the room to be 10.2 m, 10.3 m and 10.4 m across.

Were they precise? Were they accurate?

Accurate and Precise as it relates to Blood Pressure

lets say a person’s blood pressure is truly 124/78.

3 different people measure it and they get the following data

1. 110/62

2. 110/60

3. 112/62

Is this data accurate or precise, both or neither?

Accurate and Precise as it relates to Blood Pressure

lets say a person’s blood pressure is truly 124/78.

3 different people measure it and they get the following data

1. 124/58

2. 146/90

3. 98/64

Is this data accurate or precise, both or neither?

Accurate and Precise as it relates to Blood Pressure

lets say a person’s blood pressure is truly 124/78.

3 different people measure it and they get the following data

1. 126/78

2. 126/80

3. 124/76

Is this data accurate or precise, both or neither?

Types of measurement

• Quantitative- use numbers

• Qualitative- use description

• 4 feet

• extra large

• Hot

• 100ºF

Scientists prefer

• Quantitative- easy check

• Easy to agree upon, no personal bias

• The measuring instruments limit how good a measurement can be

Significant Figures

• Indicate precision of a measurement.

• Recording Sig Figs– Sig figs in a measurement include the known

digits plus a final estimated digit

2.75 cm

Significant Figurescount any # 1-9

– Zeros are tricky 00000000

– Count all numbers EXCEPT:

• Never count Leading zeros -- 0.00471 (? sig figs)

• Count all trapped zeros 12.07 (? sig figs)

• Don’t count Ending zeros unless they have a decimal point -- 7,400 (? sig figs)

• Count zeros that have a decimal point at the end 3500.

1. 32.30

Significant Figures

Counting Sig Fig Examples

2. 4002

3. 3,470

4. 0.090

Significant Figures

• Calculating with Sig Figs– Multiply/Divide - The # with the fewest sig

figs determines the # of sig figs in the answer.

(14.22g/cm3)(21.5cm3) = 305.73g

306 g

4 SF 3 SF3 SF

Significant Figures

• Calculating with Sig Figs– Multiply/Divide - The # with the fewest sig

figs determines the # of sig figs in the answer.

(17.8g/cm3)(11.53cm3) = 205.234g

205 g

3 SF 4 SF3 SF

Significant Figures

• Calculating with Sig Figs – Add/Subtract - The # with the lowest decimal

value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.8 mL 350 g

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g

Significant Figures

• Calculating with Sig Figs – Exact Conversions do not limit the # of sig figs in the answer.

• Exact conversions: 1 m = 100 cm

• 1 in = 2.54 cm

• 3 feet = 1 yard

Significant Figures

(15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

4 SF 2 SF

2.4 g/mL2 SF

Significant Figures

Practice Problems

18.1 g

18.9 g

- 0.84 g18.06 g

Scientific Notation

• Converting into Sci. Notation:

– Move decimal until there’s 1 digit to its left. Places moved = exponent. (a # 1-10)

– Large # (>1) positive exponentSmall # (<1) negative exponent

– Only include sig figs.

65,000 kg 6.5 × 104 kg

Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5 km

10. 6.2 104 mm

Practice Problems

Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5 km

10. 6.2 104 mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mm

Scientific Notation

• Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.442nd 2nd

EEEE÷÷

2nd 2nd

EEEE ENTERENTER7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your TI-30 x IIS calculator:

Scientific Notation

• Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44 n n x10x10

ENTERENTER7 (8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your TI-30XS Multiview calculator:

÷÷enter n n x10x10

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Measuring Temperature0ºC

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Measuring Temperature

Celsius scale. water freezes at 0ºC water boils at 100ºC body temperature 37ºC room temperature 20 - 25ºC

0ºC

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Convert Celsius to Fahrenheit

9/5 C + 32 = F

Ex. Convert 10 C to F

(9/5 x 10) + 32 = 50 F

33

Convert Fahrenheit to Celsius

5/9 (F – 32) = C

Ex. Convert 45 F to C

5/9 (45 – 32) = 7.2 C

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Measuring Temperature C + 273 = K K -273 = C

Convert 25 C into K

25 C + 273 = 298 K

Convert 303 K into C

303 K – 273 = 30 C

273 K

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Measuring Temperature Kelvin starts at absolute zero (-273 º C) degrees are the same size C = K -273 K = C + 273 Water freezes at 273 K Water boils at 373 K Kelvin is always bigger. Kelvin can never be negative.

273 K

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Quantity Base Unit Symbol

Length – meter m Mass - gram g Time – second s Temperature - Kelvin or ºCelsius K or C Energy - Joules J Volume - Liter L Amount of substance - mole mol

Quantity Base Unit Symbol

Length – meter m Mass - gram g Time – second s Temperature - Kelvin or ºCelsius K or C Energy - Joules J Volume - Liter L Amount of substance - mole mol

SI Units

mega- M 106

deci- d 10-1

centi- c 10-2

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

nano- n 10-9

pico- p 10-12

kilo- k 103

BASE UNIT --- 100

Million

1000

1

1/10 = .1

1/100 = .01

1/1000= .001

.000001

SI Units – Standard International

Quantity Base Unit Abbrev.

Length

Mass

Time

Temp

meter

kilogram

second

kelvin

m

kg

s

K

Amount mole mol

Symbol

l

m

t

T

n

Volume and Density

• Combination of base units.

• Volume (cm3) – length length length

D = MV

1 cm3 = 1 mL

• Density = g/cm3

– mass per volume

Density• An object has a volume of 825 cm3 and a

density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = (13.6 g/cm3)(825cm3)

M = 11,220 g

M= 11,200 gV

MD

Density• A liquid has a density of 0.87 g/mL. What

volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

WORK:

V = M D

V = 25 g =28.736

0.87 g/mL

V = 29 mLV

MD

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Converting

k h D d c m how far you have to move on this chart,

tells you how far, and which direction to move the decimal place.

The box is the base unit, meters, Liters, grams, etc.

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Conversions

Change 5.6 m to millimeters

k h D d c m

starts at the base unit and move three to the right.move the decimal point three to the right

56 00

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Conversions

Change 5.6 km to millimeters

k h D d c m

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Conversions

Change 5.6 km to millimeters Km to mm is 6 steps

5.6 E6 mm or 5,600,000 mm

k h D d c m

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Conversions

convert 25 mg to grams convert 0.45 km to mm convert 35 mL to liters

k h D d c m

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Conversions

convert 25 mg to grams .025 g convert 0.45 km to mm 450,000 mm convert 35 mL to liters .035 L

k h D d c m

100mL graduated cylinder (52.7 mL)10mL graduated cylinder (6.62 mL)

51

STOP

END HERE

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Volume calculated by multiplying L x W x H Liter the volume of a cube 1 dm (10 cm)

on a side so 1 L = 10 cm x 10 cm x 10 cm 1 L = 1000 cm3 1/1000 L = 1 cm3 1 mL = 1 cm3

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Volume 1 L about 1/4 of a gallon - a quart 1 mL is about 20 drops of water or 1

sugar cube

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Mass weight is a force, is the amount of

matter. 1gram is defined as the mass of 1 cm3

of water at 4 ºC. 1000 g = 1000 cm3 of water 1 kg = 1 L of water

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Mass 1 kg = 2.5 lbs 1 g = 1 paper clip 1 mg = 10 grains of salt or 2 drops of

water.

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Which is heavier?

it depends

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Density how heavy something is for its size the ratio of mass to volume for a

substance D = M / V Independent of how much of it you have gold - high density air low density.

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Calculating The formula tells you how units will be g/mL or g/cm3 A piece of wood has a mass of 11.2 g

and a volume of 23 mL what is the density?

A piece of wood has a density of 0.93 g/mL and a volume of 23 mL what is the mass?

59

Calculating A piece of wood has a density of 0.93 g/mL

and a mass of 23 g what is the volume? The units must always work out. Algebra 1 Get the thing you want by itself, on the top. What ever you do to onside, do to the other

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Floating Lower density floats on higher density. Ice is less dense than water. Most wood is less dense than water Helium is less dense than air. A ship is less dense than water

61

Density of water 1 g of water is 1 mL of water. density of water is 1 g/mL at 4ºC otherwise it is less

62

Measuring Temperature

Celsius scale. water freezes at 0ºC water boils at 100ºC body temperature 37ºC room temperature 20 - 25ºC

0ºC

63

Measuring Temperature Kelvin starts at absolute zero (-273 º C) degrees are the same size C = K -273 K = C + 273 Kelvin is always bigger. Kelvin can never be negative.

273 K

Dimensional Analysis• Measurement conversion

– Units cancel out, so as to convert from one unit of measurement to another unit

– but same value– Ex. which is more 36 individual doughnuts or

3 dozen doughnuts

36 doughnuts x = dozen

Dimensional Analysis

• Measurement conversion– Cancel out units and convert to unit you want

36 doughnuts x 1 dozen = dozen

12 doughnuts

Dimensional Analysis

• Measurement conversion– Multiply everything on top– divide by everything on bottom

36 doughnuts x 1 dozen = 3 dozen

12 doughnuts

Dimensional Analysis- is like multiplying by 1

units change but value stays the same

• Conversion factors always equal 1

• 1/1= 1

• 5/5= 1

• 12/dozen= 1

• 2/pair = 1

• 100cm/1meter=1

• 2.54cm/1in= 1

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

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

Dimensional Analysis 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

8.0 cm 1 in

2.54 cm= 3.1 in

cm in

Dimensional Analysis• You live 7 Kilometers from school how many

meters do you live from school?

7.00 km 1000 m

1 Km= 7000 m

Km m

Dimensional Analysis• How many milliliters are in 1.00 quart of

milk? (1L = 1.057 qt)

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L

Dimensional Analysis• Convert 445 km/hr to m/s

445 km

Km/hr m/s

hr

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

1 hr

60 min

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

1 hr

60 min

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

1 hr

60 min

1 min

60 sec=

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

1 hr

60 min

1 min

60 sec=

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

1 hr

60 min

1 min

60 sec=

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

1 hr

60 min

1 min

60 sec= 123.61

Dimensional Analysis• Convert 445 km/hr to m/s

445 km 1000 m

Km/hr m/s

hr 1 km

1 hr

60 min

1 min

60 sec= 123.61

124 m/s

Dimensional Analysis• You have 1.5 pounds of gold. Find volume in cm3 if the

density of gold is 19.3 g/cm3.• 1 Kg = 2.2 lb

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g

Dimensional Analysis

Kell football needs 550 cm for a 1st down. How many yards is this?

550 cm 1 in

2.54 cm= 6.0 yd

cm yd

1 ft

12 in

1 yd

3 ft

Percent Error• Indicates accuracy of a measurement

• Compared to Accepted Value (literature)

• That is how close your lab findings are to the accepted value

Percent Error• Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

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.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.94 %

Percent Error• A student determines the density of a

substance to be 2.95 g/mL. Find the % error if the accepted value of the density is 3.17 g/mL.

% error =

100literature

literaturealexperimenterror %

Percent Error• A student determines the density of a

substance to be 2.95 g/mL. Find the % error if the accepted value of the density is 3.17 g/mL.

% error = 6.94 %

% error = [ 2.95 g/ml – 3.17 g/ml ] x 100

3.17 g/ml

E. Proportions

• Direct Proportion

• Inverse Proportion

xy

xy

1

y

x

y

x