Importance of Measurement in Scientific Study

1. Chapter 3 – Scientific Measurement

2. Chapter Preview • 3.1 - Importance of Measurement • Qualitative/Quantitative measurements • Scientific Notation • 3.2 - Uncertainty in Measurements • Accuracy, precision, & error • SIGFIGS! • 3.3 - International System of Units • Length, Volume, Mass • Metric System • 3.4 - Density • What is it? • Calculations • 3.5 - Temperature • What is it? • Different scales

3. Section 3.1 The Importance of Measurement • Qualitative measurements – non-numerical measurements • Quantitative measurements – measurements in a definite, numerical form… ALWAYS with units. • If you don’t put a unit on an answer, it’s wrong.

4. Measurements: Qualitative or Quantitative? • 3 meters • Large trash cans • 5 car lengths • Round • Brown basketballs • 6 runs • Several slugs • 98 degrees • Millions of stars

5. Scientific Notation • In chemistry and other sciences, very small or large numbers are often used • 602,000,000,000,000,000,000,000 • Scientific notation is a method of writing these numbers in a shorter, easier form. • 6.02 x 1023

6. Scientific Notation • In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power. Scientific Notation: M x 10n 1 ≤ M ≤ 9 and n is a whole number • 6.02 x 1023 • 6.02 is the coefficient • 1023 moves the decimal place • The exponent is the number of decimal places moved

7. Scientific notation • The following are examples of where to locate the scientific notation button and on how to type scientific notation in.

15. Examples • Write each measurement in scientific notation • 5,433 → 5.433 x 103 • 665,000 • 0.000425 • 0.0000000005500

16. Standard Notation • Write the following measurements in standard notation • 3 x 104 • 0.056 x 103 • 4.56 x 10-9

17. Scientific Notation • Multiplying and dividing • To multiply: • Multiply the coefficients to get the new coefficient • Add the exponents to get the new exponent Ex: (2.0 x 103)(3.0 x 104) = 6.0 x 107 • To divide: • Divide the coefficients to get the new coefficient • Subtract the exponents to get the new exponent Ex: (10.0 x 105)/(5.0 x 102) = 2.0 x 103

18. Adding and subtracting • The decimal places must be in the same spot on the standard notation number • Align the decimal places by shifting the decimal and adjusting the exponent until the exponents are the same Ex: 45.5 x 102 + 2.5 x 103 4.55 x 103+ 2.5 x 103 • Then add or subtract. Keep the exponent Ex: 7.05 x 103

19. Examples • (6.50 x 104) x (5.0 x 106) • (6.50 x 104) x (5.0 x 10-5) • (2.3 x 103) / (4.0 x 104) • (2.3 x 103) / (4.0 x 10-4) • (2.3 x 103) + (4.0 x 105) • (2.3 x 103) - (4.0 x 105) • (6.50 x 104) - (5.0 x 10-5)

20. A scientific calculator has a scientific notation button on your calculator. It will make solving problems in chemistry much easier! • TI = Normally select the 2nd button followed by the ee button. • Casio = Normally select the exp button.

21. Section 3.2 Uncertainty in Measurements • Objectives: • Distinguish among the accuracy, precision, and error of a measurement • Identify the number of significant figures in a measurement and in the result of a calculation

22. Section 3.2 Uncertainty in Measurements • All measurements have some degree of uncertainty • Meter stick • Making precise measurements reliably is important

25. Uncertainty in Measurements • Correctness and reproducibility in measurements have certain terms. • Accuracy - how close the measurement is to the actual value. • Precision – how consistent a series of measurements is.

26. Uncertainty in Measurements

27. Uncertainty in Measurements • To evaluate the accuracy of a measurement, you observe the accepted value and experimental value • Accepted value – the correct value based on reliable references • Experimental value – the value actually measured in the lab

28. Uncertainty in Measurements • Error – the difference between the accepted and experimental value Error = experimental value – accepted value • Percent error – shows the error relative to the accepted value

29. Example • You measure the freezing temperature of water to be 2 degrees Celsius. What is the percent error of your measurement? You will need to convert to Kelvin! (Celsius + 273 = Kelvin)

30. Activity Lab: Percent Error • Get into groups of two. • Complete each station.

31. Significant Figures • Significant figures include all of the digits that are known, plus a last digit that is estimated.

32. Significant Figures Rules • Rule #1 • All nonzero digits are significant. • 456 cm • 1.982 km • Rule #2 • All zeros appearing in between nonzero digits are significant. • 2,002.3 mi • 100.5 lbs

33. Significant Figures Rules • Rule #3 • Leftmost zeros appearing in front of nonzero digits are not significant. • 0.0037 m • 0.000 009 km • Rule #4 • Rightmost zeros appearing after a nonzero digit with NO decimal are NOT significant. • 200 mi • 45,000,000 lbs

34. Significant Figures Rules • Rule #5 • Rightmost zeros appearing after a nonzero digit WITH a decimal ARE significant. • 32.00 m • 120.0 km • Rule #6 • There are two situations in which measurements have an unlimited number of significant figures. • Counting items with whole numbers. (i.e. people) • Exactly defined quantities. (60 min = 1 hour)

35. Examples • 30.0 meters • 3 sig figs • 22 meter sticks • Unlimited • 0.07080 meter • 4 sig figs • 98,000 meters • 2 sig figs • 123 meters • 3 sig figs • 0.123 meter • 3 sig figs • 40,506 meters • 5 sig figs • 9.8000 x 104 meters • 5 sig figs

36. Sig Figs in Calculations • Rounding Sig Figs • An answer cannot be more precise than the least precise measurement from which it was calculated. • To round a number, you must first decide how many significant figures the answer should have. It depends on the given measurements.

37. Rules for Rounding Numbers

38. Examples: Round each measurement to three significant figures. • 9009 m • 1.7777 x 10-3 m • 629.55 m • 87.073 m • 4.3621 x 108 m • 0.01552 m

39. Sig Figs in Calculations • Addition & Subtraction • Add / Subtract Normally • Find the least place value that all given numbers have in common • Round to that least place value.

40. Examples • 12.52 m + 349.0 m + 8.24 m • 74.626 m – 28.34 m

41. Sig Figs in Calculations • Multiplication & Division • Multiply / Divide Normally • Count the number of sig figs in each given number. • Round to the least amount of sig figs.

42. Examples • 7.55 m x 0.34 m • 2.4526 g ÷ 8.4 mL

43. Section 3.3 International System of Units • The International System of Units (SI) is a revised version of the metric system. • Le Systéme International d’Unités • It was adopted by international agreement in 1960.

44. Base Units • There are seven SI base units. From these base units, all other SI units are derived.

45. Derived Units • Derived units are made from a combination of base units. Examples include: • m3 = Volume • g/cm3 = Density • Pa = Pressure

46. Prefixes Used in the Metric System

47. Units of Length • 1 km = 1000 m • Meter (m) is base unit • 1 dm = 1/10 m 1 dm = 0.1 m • 1 cm = 1/100 m 1 cm = 0.01 m • 1 mm = 1/1000 m 1 mm = 0.001 m • 1 μm= 1/1 000 000 m 1 μm = 0.000 001 m • 1 nm = 1/1 000 000 000 m 1 nm = 0.000 000 001 m

48. Examples • Convert the following lengths: • 25 m to cm • 1.67 mm to m • 2,300 mm to km • 4.5 x 109 nm to cm

49. Units of Volume • The space occupied by any sample of matter is called its volume. • Length x width x height = volume • 1m x 1m x 1m = 1 m3 • Other useful volume units include: • Liter (L) • Milliliter (mL) • Cubic centimeter (cm3)

50. Examples • Convert the following volumes: • 35 mL to L • 2300 m3 to cm3 • 15 mL to cm3 • 25 cm3 to mm3