Chapter 2 - Measurements and Calculations

Chapter 2 - Measurements and Calculations


11

Chapter 2 - Measurements and

Calculations

Chapter 2 - Measurements and

Calculations



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Section 2.1 - Scientific MethodRead Section 1 - Going Through Very

Quickly

Section 2.1 - Scientific MethodRead Section 1 - Going Through Very

Quickly

• Observing and Collecting Data• Quantitative - Numerical

Information (25.7 grams)• Qualitative - Non-numerical (the fact

that the sky is blue)• A system is a specific portion of

matter in a given region of space that has been selected for study during and experiment or observation

• Observing and Collecting Data• Quantitative - Numerical

Information (25.7 grams)• Qualitative - Non-numerical (the fact

that the sky is blue)• A system is a specific portion of

matter in a given region of space that has been selected for study during and experiment or observation



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Scientific Method Cont-Scientific Method Cont-

• Formulating Hypothesis• Scientists use generalizations about

data to formulate a hypothesis, or testable statement.

• The hypothesis serves as a basis for making predictions and for carrying out further experiments

• Hypothesis are “if-then” statements

• Formulating Hypothesis• Scientists use generalizations about

data to formulate a hypothesis, or testable statement.

• The hypothesis serves as a basis for making predictions and for carrying out further experiments

• Hypothesis are “if-then” statements



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Scientific Method Cont-Scientific Method Cont-

• Theorizing• When data shows the predictions of the

hypothesis to be successful,Scientists try to explain by constructing a model.

• A model is a physical object built to explain a hypothesis.

• If a model successfully explains the data then it becomes part of a theory, which is a broad generalization that explains a body of facts.

• Theorizing• When data shows the predictions of the

hypothesis to be successful,Scientists try to explain by constructing a model.

• A model is a physical object built to explain a hypothesis.

• If a model successfully explains the data then it becomes part of a theory, which is a broad generalization that explains a body of facts.


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Section 2-2 Units of Measurement• Observations are either:

– Quantitative - Numerical Information (25.7 grams)– Qualitative - Non-numerical (the fact that the sky

is blue)– A system is a specific portion of matter in a given

region of space that has been selected for study during and experiment or observation

• Measurements represent quantities.

A quantity is something that has magnitude, size, or amount.

• Measurements are numbers plus a unit.• Measurements are quantitative!



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What are units?What are units?• Units are descriptors of numbers.• They give numbers meanings.• For example, the ordinary number 30.• You have no clue what the number 30

represents, it could be 30 desks, 30 pencils, or 30 books.

• You need a descriptor or a unit to tell you exactly what the number represents.

• For instance, 300C, tells us that 30 represents a temperature.

• Or, 30 meters tells us that 30 is representing a distance or a length.

• Units are descriptors of numbers.• They give numbers meanings.• For example, the ordinary number 30.• You have no clue what the number 30

represents, it could be 30 desks, 30 pencils, or 30 books.

• You need a descriptor or a unit to tell you exactly what the number represents.

• For instance, 300C, tells us that 30 represents a temperature.

• Or, 30 meters tells us that 30 is representing a distance or a length.



77

The Metric SystemThe Metric System• The metric system of measurement has

a long historical background and grew out of a need for standard and reproducible measurement for both science and commerce.

• It has two advantages over the English system of measurement.

1. Units are well defined in terms of things that are easily and accurately reproduced.2. All conversions within the system can be

preformed by moving a decimal point.

• The metric system of measurement has a long historical background and grew out of a need for standard and reproducible measurement for both science and commerce.

• It has two advantages over the English system of measurement.

1. Units are well defined in terms of things that are easily and accurately reproduced.2. All conversions within the system can be

preformed by moving a decimal point.



88

SI MeasurementSI Measurement• In 1960, modern SI Units were

established.• Scientists all over the world have

agreed on a single measurement system called

• “Le Systeme International de Unites”, abbreviated SI.

• This revision declared that only a minimum number of base units would be rigorously defined.

• These base units are……..

• In 1960, modern SI Units were established.

• Scientists all over the world have agreed on a single measurement system called

• “Le Systeme International de Unites”, abbreviated SI.

• This revision declared that only a minimum number of base units would be rigorously defined.

• These base units are……..


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There are Seven Base Units• the meter(m) for distance or length,• the kilogram(kg) for mass• the second(s) for time• the ampere(A) for electric current• the Kelvin(K) for temperature• the mole(mol) for amount of substance• the candela for intensity of light.

• All other units would be derived from these base units!!!!!!!



1010

PrefixesPrefixes

• There are several prefixes that are associated with a decimal position and can be attached to a base metric unit in order to create a new metric unit.

• The knowledge of the decimal meaning of the prefix establishes the relationship between the newly created unit and the base unit.

• Page 35 in your text. Similar Chart on next slide

• There are several prefixes that are associated with a decimal position and can be attached to a base metric unit in order to create a new metric unit.

• The knowledge of the decimal meaning of the prefix establishes the relationship between the newly created unit and the base unit.

• Page 35 in your text. Similar Chart on next slide



1111

SI Prefixes Prefix Decimal Equivalent Unit Exponential Equivalent Abbreviation_________________________ Tera 1,000,000,000,000 T 1012 Giga 1,000,000,000 G 109 Mega 1,000,000 M 106 Kilo 1,000 k 103 Hecto 100 h 102 Deka 10 da 101 BASE 1 Liter, meter, gram, second, mole 100 Deci 1/10 (0.1) d 10-1 Centi 1/100 (0.01) c 10-2

Milli 1/1000 (0.001) m 10-3 Micro 1/1,000,000 (0.000001) u 10-6 Nano 1/1,000,000,000 n 10-9 Pico 1/1,000,000,000,000 p 10-12


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Metric Conversion - The Factory Label Method (SHOW YOUR WORK!)METRIC UNIT TO BASE

2.5 cm = _______ m

2.5 cm X 1m100 cm

= 0.025 m

We know that 1m = 100 cm, so possible conversion factors are:

1m/100cm or 100cm/1m , which do I choose?

I choose 1m/100cm because I needed cm to cancel out and neededto end up with the units of meter!


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Another Example - BASE TO METRIC UNIT

34 L = ___________ ml

I know that there are 1000ml in 1 L, so I have the choice between twoconversion factors1000ml/1L or 1L/1000ml, so

I look @ the conversion and decide which one will allow me to cancel outL and end up with ml in my final answer.

34 L X 1000ml1L

= 34,000 ml


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Unit Conversion Examples - Show your work!!!!METRIC TO BASE TO METRIC

85.6 mg to kilograms

85.6 mg x 1g x 1kg = 0.00008561000mg 1000g

85.6 mg x 1kg = 0.0000856106mg

79.3 hectoliters to milliliters

79.3 hL x 100L x 1000ml = 7,930,000 ml1hL 1L


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Scientific Notation

• In scientific notation, numbers are written in the formM x 10n

Where M is a number greater than or equal to 1 but less than 10 and n is a whole number


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Rules for Scientific Notation

Scientific Notation is a short cut for writing very large or very small numbersLong form (regular numbers) to Scientific Notation

1. Is the number greater or less than 12. If it is not already, you want to position the decimal point where the number to the left is less than 10, but greater than 03. When moving the decimal from the original position to the position described in Rule 2, notice which way the point moves

a. To the right – the power or exponent of 10 will be negativeb. To the left – the exponent will be positive

4. How many places the decimal point moves is the power of 10Example:0.00045 – 4.5 x 10-4 456789 – 4.6 x 105


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Scientific Notation to Long form

1. If the exponent is negative move the decimal to the left

2. If it is positive move it to the rightExample: 2.6 x 10-3 – 0.0026

3.94 x 104 - 39400


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Mathematical Operations and Scientific NotationCalculator Operation – Will go over in class!

By Hand – I strongly suggest using your calculators for accuracy!!!

Addition/Subtraction Using Scientific NotationConvert the numbers to the same power of ten, usually the largest.Add (subtract) the nonexponential portion of the numbers.The power of ten remains the same. Example: (1.00 × 104) + (2.30 × 105)A good rule to follow is to express all numbers in the problem to the highest power of ten.Convert (1.00 × 104) to (0.100 × 105).(0.100 ×105) 1 (2.30 × 105) = 2.40 × 105


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Multiplication Using Scientific NotationThe numbers (including decimals) are multiplied.The exponents are added.The answer is converted to scientific notation—the product of a number between 1 and 10 and an exponential term. Example: (4.24 × 102) × (5.78× 104)

(4.24 × 5.78) × (102+4) = 24.5 × 106

Convert to scientific notation = 2.45 × 107

Division Using Scientific Notation

1. Divide the decimal parts of the number.2. Subtract the exponents.3. Express the answer in scientific notation.

Example: (3.78 × 105) / (6.2 × 108)(3.78 × 6.2) × (105-8) = 0.61 × 10-3

Convert to scientific notation = 6.1 × 10-4



2020

Derived SI UnitsDerived SI Units• Combinations of SI base units form

derived units.• Derived units are produced by

multiplying or dividing standard units.

• Examples(2m)(2m) = 4 m2 (meters squared)2g = 1 g/ml (grams per

milliliter)2ml

• Combinations of SI base units form derived units.

• Derived units are produced by multiplying or dividing standard units.

• Examples(2m)(2m) = 4 m2 (meters squared)2g = 1 g/ml (grams per

milliliter)2ml

A this per that number!!. There is 1 g of substance for every 1 ml.



2121

Using Scientific MeasurementsUsing Scientific Measurements

• Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. (ATV)

• Precision refers the closeness of a set of measurements of the same quantity made in the same way.

• Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. (ATV)

• Precision refers the closeness of a set of measurements of the same quantity made in the same way.


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Accuracy vs. Precision

Accepted value is the bulls eye


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These values were recorded as the mass of products when a chemical reaction was carried out three separate times: 8.83 g; 8.84 g; 8.82 g. The mass of products from that reaction is 8.60 g (Accepted Value).

Are the experimental values accurate, precise, or both?

8.60 g = the accepted agreed upon value for the reaction

8.83g, 8.84g, and 8.82g are measurements that are very close to one another!

They are PRECISE!!!!

In a laboratory setting 0.20 g is a significant deviation from the acceptedvalue!

The Experiment produced Precise, but inaccurate results!!!

They too far from the accepted value thus inaccurate!



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Percent ErrorPercent Error

• Percent Error is calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100.

• Percent Error = (Value experimental - Value accepted) X 100

Value accepted

• Percent Error is calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100.

• Percent Error = (Value experimental - Value accepted) X 100

Value accepted



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Errors in MeasurementErrors in Measurement

• Some error or uncertainty exists in any measurement

• WHY?Skill of the measurerThe conditionsThe measurement instrument

themselves

• Some error or uncertainty exists in any measurement

• WHY?Skill of the measurerThe conditionsThe measurement instrument

themselves



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Significant FiguresSignificant Figures• Sig Figs in a

measurement consists of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

• The rules for determining sig figs are located on page 47.

• Sig Figs in a measurement consists of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

• The rules for determining sig figs are located on page 47.

11.6 for certain + 5 which is estimated for a measurement of - 11.65 inches

11.65 inches


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Ex. 45689 - 5 sig figs (Rule 1)

Ex: 32002 sig figs(Rule 4)

0.0032 - 2 sig figs(Rule 2)

Remember: Zeros betweenNon zero numbers are Significant.

45.00 - 4 sig figs(Rule 3)

Rule 1


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Rules for Sig Figs By Examples

• Rule 180.67 = 4

20487 = 5

67009 = 5

12 = 2

198762534 =9

4 = 1

• Rule 20.0567 = 3

0.000001 = 1

0.034 = 2

0.01234567 = 7

0.000000023 = 2

0.12 = 2


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Rules By Example continued

• Rule 34.00 = 3

234.00 = 5

12389.000 = 8

1.20 = 3

2.4500 = 5

• Rule 4 2000 = 1

2340000 = 3

1200 = 2

1200. = 4

2000. = 4



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Addition, Subtraction, and Division with Sig

Figs

Addition, Subtraction, and Division with Sig

Figs• When adding, subtracting, or

dividing numbers, determine the number that has the least number of sig figs and record (round) your answer to that number of sig figs.

• When adding, subtracting, or dividing numbers, determine the number that has the least number of sig figs and record (round) your answer to that number of sig figs.



3131

Direct ProportionsDirect Proportions

• Two quantities are directly proportional to each other if dividing one by the other gives a constant value

• As one quantity increases so does the other

• Graph is in the shape of a straight Line

• Two quantities are directly proportional to each other if dividing one by the other gives a constant value

• As one quantity increases so does the other

• Graph is in the shape of a straight Line



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Inverse ProportionsInverse Proportions

• Two quantities are inversely proportional to each other if their product is constant

• As one goes up the other goes down

• Graph is a hyperbola

• Two quantities are inversely proportional to each other if their product is constant

• As one goes up the other goes down

• Graph is a hyperbola

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Chapter 2 - Measurements and Calculations

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