1 chapter 3 scientific measurement 2 types of measurement l quantitative- (quantity) use numbers to...

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Chapter 3

Scientific measurement

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Types of measurement Quantitative- (quantity) use numbers to

describe Qualitative- (quality) use description

without numbers 4 meters extra large Hot 100ºC

Quantitative

Qualitative

Qualitative

Quantitative

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Which do you Think Scientists would prefer

Quantitative- easy check Easy to agree upon, no personal bias The measuring instrument limits how

good the measurement is

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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

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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

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Accurate? Yes

Precise? Yes

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Precise? No

Accurate? NO

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Accurate? Yes

Precise? We cant say!

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Reporting Error in Experiment

Error• A measurement of how accurate an

experimental value is

• (Equation) Experimental Value – Accepted Value

• Experimental Value is what you get in the lab

• accepted value is the true or “real” value

• Answer may be positive or negative

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• % Error = • | experimental – accepted value | x 100

accepted value

OR | error| x 100 accepted value

• Answer is always positive

Reporting Error in Experiment

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Example: A student performs an experiment and recovers 10.50g of NaCl product. The amount they should of collected was 12.22g on NaCl.

1. Calculate Error

Error = 10.50 g - 12.22 g = - 1.72 g

2. Calculate % Error

% Error = | -1.72g | x 100 12.22g= 14.08% error

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Scientific Notation

Example: 2.5x10-4 (___) is the coefficient and ( ___) is the power of ten

2.5

-4

Convert to Scientific Notation And Vise Versa

5500000 = ____________

3.44 x 10-2 = ____________

2.16 x 103 = ____________

0.00175 = ____________

5.5 x 106

0.0344

2160

1.75 x 10-3

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Multiplying and Dividing Exponents using a calculator

(3.0 x 105) x (3.0 x 10-3) = _________________

(2.75 x 108) x (9.0 x 108) = ________________

(5.50 x 10-2) x (1.89 x 10-23) = ____________

(8.0 x 108) / (4.0 x 10-2) = ________________

9.00 x 102

2.475 x 1017

1.04 x 10-24

2.0 x 1010

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Adding and Subtracting Exponents using a calculator

7.5 x 107 + 2.5 x 109 = __________________

5.5 x 10-2 - 2.5 x 10-5 = _________________

2.575 x 109

5.498 x 10-2

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Significant figures (sig figs) How many numbers mean anything When we measure something, we can

(and do) always estimate between the smallest marks.

21 3 4 5

4.5 inches

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Significant figures (sig figs) Scientist always understand that the

last number measured is actually an estimate

21 3 4 5

4.56 inches

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Sig Figs What is the smallest mark on the ruler that

measures 142.15 cm? 142 cm? 140 cm? Here there’s a problem does the zero count

or not? They needed a set of rules to decide which

zeroes count. All other numbers do count

Tenths place

Ones place

Yikes!

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Which zeros count? Those at the end of a number before

the decimal point don’t count 12400 If the number is smaller than one,

zeroes before the first number don’t count

0.045

= 3 sig figs

= 2 sig figs

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Which zeros count? Zeros between other sig figs do. 1002 zeroes at the end of a number after the

decimal point do count 45.8300 If they are holding places, they don’t. If they are measured (or estimated) they

do

= 4 sig figs

= 6 sig figs

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Sig Figs Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12 A a piece of paper is measured 11

inches tall. Being able to locate, and count

significant figures is an important skill.

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Sig figs. How many sig figs in the following

measurements? 458 g 4085 g 4850 g 0.0485 g 0.004085 g 40.004085 g

= 3 sig figs

= 4 sig figs

= 3 sig figs

= 3 sig figs= 4 sig figs

= 8 sig figs

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Sig Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g

= 3 sig figs

= 6 sig figs= 6 sig figs

= 3 sig figs

= 4 sig figs

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Question 50 is only 1 significant figure if it really has two, how can I write it? A zero at the end only counts after the

decimal place. Scientific notation 5.0 x 101 now the zero counts.

50.0 = 3 sig figs

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Adding and subtracting with sig figs

The last sig fig in a measurement is an estimate.

Your answer when you add or subtract can not be better than your worst estimate.

have to round it to the least place of the measurement in the problem

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For example

27.93 6.4+ First line up the decimal places

27.936.4+

Then do the adding34.33

27.936.4

This answer must be rounded to the tenths place

Find the estimated numbers in the problem

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Rounding rules look at the number behind the one

you’re rounding. If it is 0 to 4 don’t change it If it is 5 to 9 make it one bigger round 45.462 to four sig figs to three sig figs to two sig figs to one sig fig

= 45.46

= 45.5= 45

= 50

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Practice 4.8 + 6.8765 520 + 94.98 0.0045 + 2.113 6.0 x 102 - 3.8 x 103 5.4 - 3.28 6.7 - .542 500 -126 6.0 x 10-2 - 3.8 x 10-3

= 11.6756 = 11.7

= 614.98 = 615

= 2.1175 = 2.118

= 3198 = 3.2 x 103

= 2.12 = 2.1

= 6.158 = 6.2

= 374

= 0.0562 = 5.6 x 10-2

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Multiplication and Division Rule is simpler Same number of sig figs in the answer

as the least in the question 3.6 x 653 2350.8 3.6 has 2 s.f. 653 has 3 s.f. answer can only have 2 s.f. 2400

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Multiplication and Division practice 4.5 / 6.245 4.5 x 6.245 9.8764 x .043 3.876 / 1983 16547 / 714

= 0.720576 = 0.72= 28.1025 = 28

= 0.4246852 = 0.42

= 0.001954614 = 0.001955

= 23.17507 = 23.2

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The Metric System Easier to use because it is …… a decimal system Every conversion is by some power of …. 10. A metric unit has two parts A prefix and a base unit. prefix tells you how many times to divide or multiply by 10.

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Base Units Length - meter more than a yard - m Mass - grams - a bout a raisin - g Time - second - s Temperature - Kelvin or ºCelsius K or C Energy - Joules- J Volume - Liter - half f a two liter bottle- L Amount of substance - mole - mol

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Prefixes Kilo K 1000 times Hecto H 100 times Deka D 10 times deci d 1/10 centi c 1/100 milli m 1/1000 kilometer - about 0.6 miles centimeter - less than half an inch millimeter - the width of a paper clip wire

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Converting

K H D d c m King Henry Drinks (basically) delicious chocolate milk

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

convert 25 mg to grams convert 0.45 km to mm convert 35 mL to liters It works because the math works, we

are dividing or multiplying by 10 the correct number of times (homework)

k h D d c m

= 0.025 g

= 450,000 mm

= 0.035 L

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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 or 1 L = 1000 cm3 1/1000 L = 1 cm3 Which means 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, Mass is the amount of matter. 1gram is defined as the mass of 1 cm3

of water at 4 ºC. 1 ml of water = 1 g 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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Density how heavy something is for its size the ratio of mass to volume for a

substance D = M / V

M

VD

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Density is a Physical Property The density of an object remains _________ at _______ ________ Therefore it is possible to identify an

unknown by figuring out its density.

Story & Demo (king and his gold crown)

constant constant temperature

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What would happen to density if temperature decreased?

As temperature decreases molecules ______ _____ And come closer together therefore

making volume _________ The mass ______ ____ _______ Therefore the density would _______ Exception _____________________ Therefore Density decreases ICE FLOATS

slow down

decrease

STAYS

THE SAME

INCREASE

WATER, because it expands.

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Units for Density 1. Regularly shaped object in which a

ruler is used. ______

2. liquid, granular or powdered solid in which a graduated cylinder is used ______

3. irregularly shaped object in which the water displacement method must be used _____

g/cm3

g/ml

g/ml

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Sample Problem: What is the density of a sample of

Copper with a mass of 50.25g and a volume of 6.95cm3?

D = M/V D = 50.25g / 6.95 cm3

= 7.2302 = 7.23 cm3

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Sample Problem 2. A piece of wood has a density of

0.93 g/ml and a volume of 2.4 ml What is its mass?

D

M

V

M = D x V

M = 0.93 g/ml x 2.4 ml

= 2.232 = 2.2 g

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Problem Solving or Dimensional Analysis Identify the unknown What is the problem asking for List what is given and the equalities needed to

solve the problem. Ex. 1 dozen = 12 Plan a solution Equations and steps to solve (conversion factors) Do the calculations Check your work: Estimate; is the answer reasonable UNITS All measurements need a NUMBER & A UNIT!!

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Dimensional Analysis Use the units (__________) to help analyze

(______) the problem.

Conversion Factors: Ratios of equal measurements. Numerator measurement = Denominator measurement

Using conversion factors does not change the value of the measurement

Examples; 1 ft = _____ (_________)

1 ft__ or 12 in (_____________ __________)

12 in 1 ft

dimensionssolve

12 in equality

Conversion

factors

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What you are being asked to solve for in the problem will determine which

conversion factors need to be used. Common Equalities and their conversion factors:

1 lb = _____oz

1 mi = ______ft

1 yr = ______days

1 day = ____hrs

1 hr = ____min

1 min = ____sec

16

5280

365

24

60

60

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Sample Problems using Conversion Factors: How many inches are in 12 miles?

Equalities: 1 mi = 5280 ft

1 ft = 12 in 12miles X X =

sig figs = 760,000 inches

5280 ft 1 mi

12 in 1 ft

760,320 inches

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2. How many seconds old is a 17 year old?

Equalities: 1 yr = 365 days; 1 day = 24 hrs; 1 hr = 60 min; 1 min = 60

sec 17 yrs X X X X

= 536,112,000 sec

Sig figs = 540,000,000 sec

60 sec 1 min

365 day 1 yr

60 min 1 hr

24 hrs 1 day

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3. How many cups of water are in 5.2 lbs of water?

Equalities: 1 lb = 16 oz; 8 oz = 1 cup

5.2 lbs X X =

= 10.4 cups

Sig figs = 1.0 x 101 cups

16 oz 1 lb

1 cup 8 oz

83.2 cup 8

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3. If the density of Mercury (Hg) at 20°C is 13.6 g/ml. What is it’s density in mg/L?

Equalities: 1 g = 1000 mg; 1 L = 1000 ml

X X =

13.6 g 1 ml

1000 mg 1 g

1000 ml 1 L

13,600,000 mg/L

13.6 x 107 mg/L