Chapter 2 Scientific Measurement

Chapter 2 Goals Calculate values from measurements using the correct number of significant figures. Calculate values from measurements using the correct number of significant figures. List common SI units of measurement and common prefixes used in the SI system. List common SI units of measurement and common prefixes used in the SI system. Distinguish mass, volume, density, and specific gravity from one another. Distinguish mass, volume, density, and specific gravity from one another. Evaluate the accuracy of measurements using appropriate methods. Evaluate the accuracy of measurements using appropriate methods.

Introduction Everyone uses measurements in some form Everyone uses measurements in some form Deciding how to dress based on the temperature; measuring ingredients for a recipes; construction. Deciding how to dress based on the temperature; measuring ingredients for a recipes; construction. Measurement is also fundamental in the sciences and for understanding scientific concepts Measurement is also fundamental in the sciences and for understanding scientific concepts It is important to be able to take good measurements and to decide whether a measurement is good or bad It is important to be able to take good measurements and to decide whether a measurement is good or bad

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

2.1 The Importance of Measurement Qualitative versus Quantitative Measurements Qualitative versus Quantitative Measurements Qualitative measurements give results in a descriptive, nonnumeric form; can be influenced by individual perception Qualitative measurements give results in a descriptive, nonnumeric form; can be influenced by individual perception Example: This room feels cold. Example: This room feels cold.

2.1 The Importance of Measurement Qualitative versus Quantitative Measurements Qualitative versus Quantitative Measurements Quantitative measurements give results in definite form usually, using numbers; these types of measurements eliminate personal bias by using measuring instruments. Quantitative measurements give results in definite form usually, using numbers; these types of measurements eliminate personal bias by using measuring instruments. Example: Using a thermometer, I determined that this room is 24°C (~75°F) Example: Using a thermometer, I determined that this room is 24°C (~75°F) Measurements can be no more reliable than the measuring instrument. Measurements can be no more reliable than the measuring instrument.

2.1 Concept Practice 1. You measure 1 liter of water by filling an empty 2- liter soda bottle half way. How can you improve the accuracy of this measurement? 2. Classify each measurement as qualitative or quantitative. a. The basketball is brown b. the diameter of the basketball is 31 centimeters c. The air pressure in the basketball is 12 lbs/in 2 d. The surface of the basketball has indented seams

2.2 Accuracy and Precision Good measurements in the lab are both correct (accurate) and reproducible (precise) Good measurements in the lab are both correct (accurate) and reproducible (precise) accuracy – how close a single measurement comes to the actual dimension or true value of whatever is measured accuracy – how close a single measurement comes to the actual dimension or true value of whatever is measured precision – how close several measurements are to the same value precision – how close several measurements are to the same value Example: Figure 2.2, page 29 – Dart boards…. Example: Figure 2.2, page 29 – Dart boards….

2.2 Accuracy and Precision All measurements made with instruments are really approximations that depend on the and the skill of the person doing the measurement (precision) All measurements made with instruments are really approximations that depend on the quality of the instruments (accuracy) and the skill of the person doing the measurement (precision) The precision of the instrument depends on the how small the scale is on the device. The precision of the instrument depends on the how small the scale is on the device. The finer the scale the more precise the instrument. The finer the scale the more precise the instrument. 2.2 Demo, page Demo, page 28

2.2 Concept Practice 3. Which of these synonyms or characteristics apply to the concept of accuracy? Which apply to the concept of precision? a. multiple measurements b. correct c. repeatable d. reproducible e. single measurement f. true value

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

2.3 Scientific Notation In chemistry, you will often encounter numbers that are very large or very small In chemistry, you will often encounter numbers that are very large or very small One atom of gold = g One atom of gold = g One gram of H = 301,000,000,000,000,000,000,000 H molecules One gram of H = 301,000,000,000,000,000,000,000 H molecules Writing and using numbers this large or small is calculations can be difficult Writing and using numbers this large or small is calculations can be difficult It is easier to work with these numbers by writing them in exponential or scientific notation It is easier to work with these numbers by writing them in exponential or scientific notation

2.3 Scientific Notation scientific notation – a number is written as the product of two numbers: a coefficient and a power of ten scientific notation – a number is written as the product of two numbers: a coefficient and a power of ten Example: 36,000 is written in scientific notation as 3.6 x 10 4 or 3.6e4 Example: 36,000 is written in scientific notation as 3.6 x 10 4 or 3.6e4 Coefficient = 3.6 → a number greater than or equal to 1 and less than 10. Coefficient = 3.6 → a number greater than or equal to 1 and less than 10. Power of ten / exponent = 4 Power of ten / exponent = x 10 4 = 3.6 x 10 x 10 x 10 x 10 = 36, x 10 4 = 3.6 x 10 x 10 x 10 x 10 = 36,000

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

2.3 Scientific Notation Numbers less than one have a negative exponent when written in scientific notation. Numbers less than one have a negative exponent when written in scientific notation. Example: is written in scientific notation as 8.1 x Example: is written in scientific notation as 8.1 x x = 8.1/(10 x 10 x 10) = x = 8.1/(10 x 10 x 10) = When writing a number less than one in scientific notation, the value of the exponent equals the number of places you move the decimal to the right. When writing a number less than one in scientific notation, the value of the exponent equals the number of places you move the decimal to the right.

2.3 Scientific Notation To multiply numbers written in scientific notation, multiply the coefficients and add the exponents. To multiply numbers written in scientific notation, multiply the coefficients and add the exponents. (3 x 10 4 ) x (2 x 10 2 ) = (3 x 2) x = 6 x 10 6 (3 x 10 4 ) x (2 x 10 2 ) = (3 x 2) x = 6 x 10 6 To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator (bottom) from the exponent in the numerator (top). To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator (bottom) from the exponent in the numerator (top). (6 x 10 3 )/(2 x 10 2 ) = (6/2) x = 3 x 10 1 (6 x 10 3 )/(2 x 10 2 ) = (6/2) x = 3 x 10 1

2.3 Scientific Notation Before numbers written in scientific notation are added or subtracted, the exponents must be made the same (as a part of aligning the decimal points). Before numbers written in scientific notation are added or subtracted, the exponents must be made the same (as a part of aligning the decimal points). (5.4 x 10 3 )+(6 x 10 2 ) = (5.4 x 10 3 )+(0.6 x 10 3 ) (5.4 x 10 3 )+(6 x 10 2 ) = (5.4 x 10 3 )+(0.6 x 10 3 ) = ( ) x 10 3 = 6.0 x 10 3 = ( ) x 10 3 = 6.0 x 10 3

2.3 Concept Practice 5. Write the two measurements given in the first paragraph of this section in scientific notation. a. mass of a gold atom = g b. molecules of hydrogen = 301,000,000,000,000,000,000,000 H molecules

2.3 Concept Practice 6. Write these measurements in scientific notation. The abbreviation m stands for meter, a unit of length. a. The length of a football field, 91.4 m b. The diameter of a carbon atom, m c. The radius of the Earth, 6,378,000 m d. The diameter of a human hair, m e. The average distance between the centers of the sun and the Earth, 149,600,000,000 m

2.1 Concept Practice 1. You measure 1 liter of water by filling an empty 2- liter soda bottle half way. How can you improve the accuracy of this measurement? A: Use a more precise volumetric measure such as a measuring cup.

2.1 Concept Practice 2. Classify each measurement as qualitative or quantitative. a. The basketball is brown b. the diameter of the basketball is 31 centimeters - Quantitative - Quantitative c. The air pressure in the basketball is 12 lbs/in 2 - Quantitative - Quantitative d. The surface of the basketball has indented seams - Qualitative - Qualitative - Qualitative

2.2 Concept Practice 3. Which of these synonyms or characteristics apply to the concept of accuracy? Which apply to the concept of precision? a. multiple measurements b. correct c. repeatable d. reproducible e. single measurement f. true value - Accuracy - Precision

2.2 Concept Practice 4. Under what circumstances could a series of measurements of the same quantity be precise but inaccurate? A: when using an improperly calibrated measuring device

2.3 Concept Practice 5. Write the two measurements given in the first paragraph of this section in scientific notation. a. mass of a gold atom = g b. molecules of hydrogen = 301,000,000,000,000,000,000,000 H molecules = 3.01 x H molecules = 3.27 x g

2.3 Concept Practice 6. Write these measurements in scientific notation. The abbreviation m stands for meter, a unit of length. a. The length of a football field, 91.4 m b. The diameter of a carbon atom, m c. The radius of the Earth, 6,378,000 m d. The diameter of a human hair, m e. The average distance between the centers of the sun and the Earth, 149,600,000,000 m = 9.14 x 10 1 m = 1.54 x m = x 10 6 m = 8 x m = x m