Chapter 2Chapter 2

Scientific MeasurementScientific Measurement

Chapter 2 GoalsChapter 2 Goals

Calculate values from measurements using Calculate values from measurements using the correct number of significant figures.the correct number of significant figures.

List common SI units of measurement and List common SI units of measurement and common prefixes used in the SI system.common prefixes used in the SI system.

Distinguish mass, volume, density, and Distinguish mass, volume, density, and specific gravity from one another.specific gravity from one another.

Evaluate the accuracy of measurements Evaluate the accuracy of measurements using appropriate methods.using appropriate methods.

IntroductionIntroduction

Everyone uses measurements in some formEveryone uses measurements in some form Deciding how to dress based on the Deciding how to dress based on the

temperature; measuring ingredients for a temperature; measuring ingredients for a recipes; construction.recipes; construction.

Measurement is also fundamental in the Measurement is also fundamental in the sciences and for understanding scientific sciences and for understanding scientific conceptsconcepts It is important to be able to take good It is important to be able to take good

measurements and to decide whether a measurements and to decide whether a measurement is good or badmeasurement is good or bad

IntroductionIntroduction

In this class we will make In this class we will make measurements and express their measurements and express their values using the International values using the International System of Units or the System of Units or the SI systemSI system.. All measurements have two parts: a All measurements have two parts: a

numbernumber and a and a unitunit..

2.1 The Importance of 2.1 The Importance of MeasurementMeasurement

QualitativeQualitative versus versus QuantitativeQuantitative MeasurementsMeasurements Qualitative measurementsQualitative measurements give give

results in a descriptive, nonnumeric results in a descriptive, nonnumeric form; can be influenced by individual form; can be influenced by individual perceptionperception

Example: This room feels cold.Example: This room feels cold.

2.1 The Importance of 2.1 The Importance of MeasurementMeasurement

QualitativeQualitative versus versus QuantitativeQuantitative MeasurementsMeasurements Quantitative measurements Quantitative measurements give results in give results in

definite form usually, using numbers; these definite form usually, using numbers; these types of measurements eliminate personal bias types of measurements eliminate personal bias by using measuring instruments.by using measuring instruments.

Example: Using a thermometer, I determined Example: Using a thermometer, I determined that this room is 24°C (~75°F)that this room is 24°C (~75°F)

Measurements can be no more Measurements can be no more reliable than the measuring reliable than the measuring instrument.instrument.

2.1 Concept Practice2.1 Concept Practice1. You measure 1 liter of water by filling an 1. You measure 1 liter of water by filling an

empty 2-liter soda bottle half way. How can you empty 2-liter soda bottle half way. How can you improve the accuracy of this measurement?improve the accuracy of this measurement?

2. Classify each measurement as qualitative or 2. Classify each measurement as qualitative or quantitative.quantitative.a. The basketball is browna. The basketball is brownb. the diameter of the basketball is 31 b. the diameter of the basketball is 31 centimeterscentimetersc. The air pressure in the basketball is 12 lbs/inc. The air pressure in the basketball is 12 lbs/in22

d. The surface of the basketball has indented d. The surface of the basketball has indented seamsseams

2.2 Accuracy and 2.2 Accuracy and PrecisionPrecision

Good measurements in the lab are both Good measurements in the lab are both correct correct (accurate)(accurate) and reproducible and reproducible (precise)(precise) accuracyaccuracy – how close a single measurement – how close a single measurement

comes to the actual dimension or true value comes to the actual dimension or true value of whatever is measuredof whatever is measured

precisionprecision – how close several – how close several measurements are to the same valuemeasurements are to the same value

Example: Figure 2.2, page 29 – Dart Example: Figure 2.2, page 29 – Dart boards….boards….

2.2 Accuracy and 2.2 Accuracy and PrecisionPrecision

All measurements made with instruments All measurements made with instruments are really approximations that depend on are really approximations that depend on the the quality of the instruments (accuracy) and the and the skill of the person doing the skill of the person doing the measurement measurement (precision)(precision)

The precision of the instrument depends The precision of the instrument depends on the how small the scale is on the device. on the how small the scale is on the device. The finer the scale the more precise the The finer the scale the more precise the

instrument.instrument. 2.2 Demo, page 282.2 Demo, page 28

2.2 Concept Practice2.2 Concept Practice3. Which of these synonyms or 3. Which of these synonyms or

characteristics apply to the concept characteristics apply to the concept of accuracy? Which apply to the of accuracy? Which apply to the concept of precision?concept of precision?

a. multiple measurementsa. multiple measurements

b. correctb. correct

c. repeatablec. repeatable

d. reproducibled. reproducible

e. single measuremente. single measurement

f. true valuef. true value

2.2 Concept Practice2.2 Concept Practice

4. Under what circumstances could a 4. Under what circumstances could a series of measurements of the same series of measurements of the same quantity be precise but inaccurate?quantity be precise but inaccurate?

2.3 Scientific Notation2.3 Scientific Notation In chemistry, you will often encounter In chemistry, you will often encounter

numbers that are very large or very smallnumbers that are very large or very small One atom of gold = One atom of gold =

0.000000000000000000000327g0.000000000000000000000327g One gram of H = One gram of H =

301,000,000,000,000,000,000,000 H molecules301,000,000,000,000,000,000,000 H molecules Writing and using numbers this large or Writing and using numbers this large or

small is calculations can be difficultsmall is calculations can be difficult It is easier to work with these numbers by It is easier to work with these numbers by

writing them in writing them in exponentialexponential or or scientific scientific notationnotation

2.3 Scientific Notation2.3 Scientific Notation scientific notationscientific notation – a number is – a number is

written as the product of two numbers: a written as the product of two numbers: a coefficient and a power of tencoefficient and a power of ten

Example: 36,000 is written in scientific Example: 36,000 is written in scientific notation as 3.6 x 10notation as 3.6 x 1044 or 3.6e4 or 3.6e4 Coefficient = 3.6 → a number greater than Coefficient = 3.6 → a number greater than

or equal to 1 and less than 10.or equal to 1 and less than 10. Power of ten / exponent = 4Power of ten / exponent = 4 3.6 x 103.6 x 1044 = 3.6 x 10 x 10 x 10 x 10 = 36,000 = 3.6 x 10 x 10 x 10 x 10 = 36,000

2.3 Scientific Notation2.3 Scientific Notation

When writing numbers greater than When writing numbers greater than ten in scientific notation ten in scientific notation the the exponent is positive and equal to exponent is positive and equal to the number of places that the the number of places that the exponent has been moved to the exponent has been moved to the leftleft..

2.3 Scientific Notation2.3 Scientific Notation

Numbers less than one have a Numbers less than one have a negative negative exponentexponent when written in scientific when written in scientific notation.notation. Example: 0.0081 is written in scientific Example: 0.0081 is written in scientific

notation as 8.1 x 10notation as 8.1 x 10-3-3

8.1 x 108.1 x 10-3-3 = 8.1/(10 x 10 x 10) = 0.0081 = 8.1/(10 x 10 x 10) = 0.0081 When writing a number less than one in When writing a number less than one in

scientific notation, scientific notation, the value of the the value of the exponent equals the number of exponent equals the number of places you move the decimal to the places you move the decimal to the rightright..

2.3 Scientific Notation2.3 Scientific Notation To To multiplymultiply numbers written in scientific numbers written in scientific

notation, notation, multiply the coefficients and multiply the coefficients and add the exponentsadd the exponents.. (3 x 10(3 x 1044) x (2 x 10) x (2 x 1022) = (3 x 2) x 10) = (3 x 2) x 104+24+2 = 6 x 10 = 6 x 1066

To To dividedivide numbers written in scientific numbers written in scientific notation, notation, divide the coefficients and divide the coefficients and subtract the exponent in the subtract the exponent in the denominator (bottom) from the denominator (bottom) from the exponent in the numerator (top)exponent in the numerator (top).. (6 x 10(6 x 1033)/(2 x 10)/(2 x 1022) = (6/2) x 10) = (6/2) x 103-23-2 = 3 x 10 = 3 x 1011

2.3 Scientific Notation2.3 Scientific Notation

Before numbers written in scientific Before numbers written in scientific notation are notation are addedadded or or subtractedsubtracted, , the exponents must be made the the exponents must be made the same same (as a part of aligning the (as a part of aligning the decimal points).decimal points). (5.4 x 10(5.4 x 1033)+(6 x 10)+(6 x 1022) = (5.4 x 10) = (5.4 x 1033)+(0.6 )+(0.6

x 10x 1033) )

= (5.4 + 0.60) x 10= (5.4 + 0.60) x 1033 = 6.0 x 10 = 6.0 x 1033

2.3 Concept Practice2.3 Concept Practice

5. Write the two measurements given 5. Write the two measurements given in the first paragraph of this section in the first paragraph of this section in scientific notation.in scientific notation.

a. mass of a gold atom = a. mass of a gold atom = 0.000000000000000000000327g0.000000000000000000000327g

b. molecules of hydrogen =b. molecules of hydrogen =

301,000,000,000,000,000,000,000 H 301,000,000,000,000,000,000,000 H moleculesmolecules

2.3 Concept Practice2.3 Concept Practice6. Write these measurements in scientific 6. Write these measurements in scientific

notation. The abbreviation m stands for notation. The abbreviation m stands for meter, a unit of length.meter, a unit of length.a. The length of a football field, 91.4 m a. The length of a football field, 91.4 m b. The diameter of a carbon atom, b. The diameter of a carbon atom, 0.000000000154 m0.000000000154 m c. The radius of the Earth, 6,378,000 mc. The radius of the Earth, 6,378,000 md. The diameter of a human hair, 0.000008 d. The diameter of a human hair, 0.000008 m m e. The average distance between the e. The average distance between the centers of the sun and the Earth, centers of the sun and the Earth, 149,600,000,000 m149,600,000,000 m

2.1 Concept Practice2.1 Concept Practice1. You measure 1 liter of water by filling 1. You measure 1 liter of water by filling

an empty 2-liter soda bottle half way. an empty 2-liter soda bottle half way. How can you improve the accuracy of How can you improve the accuracy of this measurement?this measurement?

A: Use a more precise volumetric A: Use a more precise volumetric measure such as a measuring cup.measure such as a measuring cup.

2.1 Concept Practice2.1 Concept Practice

2. Classify each measurement as qualitative or 2. Classify each measurement as qualitative or quantitative.quantitative.a. The basketball is brown a. The basketball is brown b. the diameter of the basketball is 31 b. the diameter of the basketball is 31 centimeterscentimeters - Quantitative- Quantitativec. The air pressure in the basketball is 12 c. The air pressure in the basketball is 12 lbs/inlbs/in22

- Quantitative- Quantitatived. The surface of the basketball has indented d. The surface of the basketball has indented seamsseams

- Qualitative- Qualitative

- Qualitative- Qualitative

2.2 Concept Practice2.2 Concept Practice3. Which of these synonyms or 3. Which of these synonyms or

characteristics apply to the concept characteristics apply to the concept of accuracy? Which apply to the of accuracy? Which apply to the concept of precision?concept of precision?

a. multiple measurementsa. multiple measurements

b. correctb. correct

c. repeatablec. repeatable

d. reproducibled. reproducible

e. single measuremente. single measurement

f. true valuef. true value

- Accuracy- Accuracy

- Accuracy- Accuracy

- Accuracy- Accuracy

- Precision- Precision

- Precision- Precision

- Precision- Precision

2.2 Concept Practice2.2 Concept Practice

4. Under what circumstances could a 4. Under what circumstances could a series of measurements of the same series of measurements of the same quantity be precise but inaccurate?quantity be precise but inaccurate?

A: when using an improperly A: when using an improperly calibrated measuring devicecalibrated measuring device

2.3 Concept Practice2.3 Concept Practice

5. Write the two measurements given in 5. Write the two measurements given in the first paragraph of this section in the first paragraph of this section in scientific notation.scientific notation.

a. mass of a gold atom = a. mass of a gold atom = 0.000000000000000000000327g0.000000000000000000000327g

b. molecules of hydrogen =b. molecules of hydrogen =

301,000,000,000,000,000,000,000 H 301,000,000,000,000,000,000,000 H moleculesmolecules

= 3.01 x 10= 3.01 x 102323 H molecules H molecules

= 3.27 x 10= 3.27 x 10-22-22gg

2.3 Concept Practice2.3 Concept Practice6. Write these measurements in 6. Write these measurements in

scientific notation. The abbreviation m scientific notation. The abbreviation m stands for meter, a unit of length.stands for meter, a unit of length.a. The length of a football field, 91.4 m a. The length of a football field, 91.4 m

b. The diameter of a carbon atom, 0.000000000154 b. The diameter of a carbon atom, 0.000000000154 m m

c. The radius of the Earth, 6,378,000 mc. The radius of the Earth, 6,378,000 m

d. The diameter of a human hair, 0.000008 m d. The diameter of a human hair, 0.000008 m

e. The average distance between the centers of the e. The average distance between the centers of the sun and the Earth, 149,600,000,000 msun and the Earth, 149,600,000,000 m

= 9.14 x 10= 9.14 x 1011 m m

= 1.54 x 10= 1.54 x 10-10-10 m m

= 6.378 x 10= 6.378 x 1066 m m

= 8 x 10= 8 x 10-6-6 m m

= 1.496 x 10= 1.496 x 101111 m m