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Chemistry Mrs. Algier Do Now: Complete the Chapter 2 vocabulary worksheet.

Learn the rules for determining significant figures in measurements and their importance in calculations. Engage in a hands-on activity to practice measuring and calculating area. Enhance your precision in reporting measurements.

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Chemistry Mrs. Algier Do Now: Complete the Chapter 2 vocabulary worksheet.

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  1. Chemistry Mrs. Algier Do Now: Complete the Chapter 2 vocabulary worksheet.

  2. YWBAT • Explain the concepts that will be on the chapter 1 & 2 test. • Determine the correct number of significant figures in a measurement.

  3. Activity Work with a partner to… • Get a ruler and index card. • Measure the length and width of the index card provided. • Calculate the area of the card.

  4. What are different tools you can use to measure?

  5. What different units have you used when measuring?

  6. Measurement • A measurement is a quantity that has both a number and a unit Examples: • Height (61 inches) • Age (17 years) • Temperature (85 deg F)

  7. Significant Figures • All measurements have some uncertainty. • The “certain” digits are called significant figures • The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. • The estimated digit is considered significant because it is reasonably reliable

  8. Significant Figures • Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.

  9. Determining Significant Figures • To determine whether a digit in a measured value is significant, you need to apply the following rules. • Every nonzero digit is assumed to be significant. Each of these measurements has three significant figures: 24.7 meters 0.743 meter 714 meters

  10. Determining Significant Figures 2. Zeros between nonzero digits are significant. Each of these measurements has four significant figures: 7003 meters 40.79 meters 1.503 meters

  11. Determining Significant Figures 3. Leftmost zeros in front of nonzero digits are NOT significant. They are placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros. Each of these measurements has only two significant figures: 0.0071 meter = 7.1 x 10-3 meter 0.42 meter = 4.2 x 10-1 meter 0.000099 meter = 9.9 x 10-5 meter

  12. Determining Significant Figures 4. Zeros at the end of a number and to the right of a decimal point are always significant. Each of these measurements has four significant figures: 43.00 meters 1.010 meters 9.000 meters

  13. Determining Significant Figures 5. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are NOT significant if they serve as placeholders to show the magnitude of the number. The zeros in these measurements are not significant: 300 meters (1 significant figure) 7000 meters(1 significant figure) 27,210 meters(4 significant figures)

  14. Determining Significant Figures 5. (continued). If such zeros were known measured values, then they would be significant. Writing the value in scientific notation makes it clear if these zeros are significant. The zeros in this measurement are significant. 300 meters = 3.00 x 102 meters (three significant figures)

  15. Determining Significant Figures There are two situations in which numbers have an unlimited number of significant figures. 6a. A number that is counted is exact. It has an unlimited number of significant figures. This measurement is a counted value, so it has an unlimited number of significant figures. 24 people in your classroom

  16. Determining Significant Figures 6b. Exactly defined quantities (such as those found within a system of measurement) have an unlimited number of significant figures. Each of these numbers has an unlimited number of significant figures. 60 min = 1 hr 100 cm = 1 m

  17. YWBAT • Determine the correct number of significant figures in a measurement. • Add and subtract with significant figures. • Multiply and divide with significant figures.

  18. Determining Significant Figures • Every nonzero digit • Zeros between nonzero digits • Zeros at the end of a number and to the right of a decimal point. • A number that is counted or is a defined quantity has unlimited significant figures. _____________________________________________ • Leftmost zeros in front of nonzero digits are NOT significant. They are placeholders. • Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are NOT significant.

  19. Determining Significant Figures How many significant figures are in each measurement? • 123 m • 40,506 mm • 9.8000 x 104 m • 22 metersticks • 0.07080 m • 98,000 m

  20. Determining Significant Figures How many significant figures are in each measurement? • 123 m 3 significant figures • 40,506 mm 5 significant figures • 9.8000 x 104 m 5 significant figures • 22 metersticksunlimited sig. figs. • 0.07080 m 4 significant figures • 98,000 m 2 significant figures

  21. Significant Figures in Calculations • A calculated answer cannot be more precise than the least precise measurement from which it was calculated. • The calculated value must be rounded to make it consistent with the measurements from which it was calculated.

  22. Significant Figures in Calculations Rounding – to round a number, you must first decide how many significant figures the answer should have. • Once you know the number of significant figures your answer should have, round to that many digits, counting from the left.

  23. Significant Figures in Calculations Rounding • If the digit immediately to the right of the last significant digit is less than 5, it is simply dropped and the value of the last significant digit stays the same. • Example: 62.5347 rounded to 4 sig figs is 62.53 • If the digit in question is 5 or greater, the value of the digit in the last significant place is increased by 1. • Example: 3.78721 rounded to 3 sig figs is 3.79

  24. Rounding Practice 1. Round 55.234579 to 4 significant digits 2. Round 0.00052786 to 3 significant digits 3. Round 25.98 to 2 significant digits 4. Round 90.096 to 4 significant digits 5. Round 55.35 to 3 significant digits

  25. Addition & Subtraction With Significant Figures • The answer should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. Examples: 12.52 m + 349.0 m + 8.24 m = 74.626 m – 28.34 m =

  26. Addition & Subtraction With Significant Figures • The answer should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. Examples: 12.52 m + 349.0 m + 8.24 m = 369.8 m 74.626 m – 28.34 m = 46.29 m

  27. Multiplying & Dividing With Significant Figures • The answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures. • Examples: • 7.55 meters x 0.34 meter = • 2.10 meters x 0.70 meter = • 2.4526 meters2 ÷ 8.4 meters = • 0.365 meters2 ÷ 0.0200 meter =

  28. Multiplying & Dividing With Significant Figures • The answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures. • Examples: • 7.55 meters x 0.34 meter = 2.6 meters2 • 2.10 meters x 0.70 meter = 1.5 meters2 • 2.4526 meters2 ÷ 8.4 meters = 0.29 meters • 0.365 meters2 ÷ 0.0200 meter = 18.3 meters

  29. Activity Follow Up • Re-measure the length and width of your index card (in cm). • Re-calculate the area of your index card. • Is your answer different than before?

  30. Activity Follow Up • Re-measure the length and width of your index card (in cm). 7.60 cm x 12.70 cm • Re-calculate the area. 96.5 cm2 • Is your answer different than before?

  31. Scientific Notation • Chemistry requires you to make accurate and often very small or very large measurements. • 1 gram of hydrogen contains 602,000,000,000,000,000,000,000 atoms of hydrogen • We use scientific notation to write very large or very small numbers more easily.

  32. Scientific Notation • In scientific notation, a number is written as the product of two numbers: • a coefficient • 10 raised to a power (exponent) • Example • 602,000,000,000,000,000,000,000 can be written as 6.02 x 1023 • The coefficient is 6.02. • The power of 10, or exponent, is 23.

  33. Scientific Notation • Coefficient: number greater than or equal to one and less than ten (1-9.99) • 10 raised to a power (exponent) • Positive exponent indicates how many times the coefficient is multiplied by 10 (number greater than 1) • Negative exponent indicates how many times the coefficient is divided by 10 (number less than 1)

  34. Scientific Notation When writing numbers greater than ten in scientific notation, the exponent is positive and equals the number of places that the original decimal point has been moved to the left. 6,300,000. = 6.3 x 106 94,700. = 9.47 x 104

  35. Scientific Notation Numbers less than one have a negative exponent when written in scientific notation. The value of the exponent equals the number of places the decimal has been moved to the right. 0.000008 = 8 x 10–6 0.00736 = 7.36 x 10–3

  36. Scientific Notation Practice Write each of these numbers in scientific notation. • 800,000 = • 0.00056 = • 9,000,000 = • 0.01234 =

  37. From Scientific to Standard Notation Write each of these numbers in standard notation. • 9.8 x 104 = • 9.8 x 10-4 = • 1.23 x 106 =

  38. Scientific Notation Multiplication To multiply numbers written in scientific notation, multiply the coefficients and add the exponents. (3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106 (2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4

  39. Scientific Notation Division To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator. Example 3.0 x 105 3.0 6.0 x 102 6.0 ( ) = = x 105–2 0.5 x 103 =5.0 x 102

  40. Scientific Notation Addition & Subtraction If you want to add or subtract numbers expressed in scientific notation and you are not using a calculator, then the exponents must be the same. • In other words, the decimal points must be aligned before you add or subtract the numbers.

  41. Scientific Notation Addition & Subtraction For example, when adding 5.4 x 103 and 8.0 x 102, first rewrite the second number so that the exponent is a 3. Then add the numbers. (5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103) = (5.4 + 0.80) x 103 = 6.2 x 103

  42. Accuracy Precision Error

  43. Accuracy and Precision • In chemistry, the meanings of accuracy and precision are quite different. • Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. • Precision is a measure of how close a series of measurements are to one another, irrespective of the actual value.

  44. Accuracy and Precision Good Accuracy, Good Precision Poor Accuracy, Good Precision Poor Accuracy, Poor Precision The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.

  45. Activity

  46. Error = experimental value – accepted value Determining Error Accepted Value – correct value for a measurement based on reliable references. Experimental Value – value measured in the lab/experiment. Error – difference between the experimental value and the accepted value. Can be positive or negative.

  47. error x 100% Percent error = accepted value Determining Error Percent Error – absolute value of the error divided by the accepted value, multiplied by 100%

  48. Determining Error Practice • A thermometer in boiling water reads 99.1°C. • Calculate the error • Calculate the percent error

  49. Determining Error Practice • A thermometer in boiling water reads 99.1°C. • Calculate the error = -0.9°C • Calculate the percent error = 0.9%

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