Significant Figures in measurements and calculations significant figures

Significant Figures in measurements and calculations

significant figures objective I can determine precision of a number using “sig figs” I can calculate using the correct precision i. e. correct “sig figs”

Significant Figures in Measurements . What are Significant Figures? Significant Figures convey important information about the precision of a measurement. In measurements, Significant Figures are all the digits that can be known precisely in a measurement, plus a last estimated digit.

Significant Figures in Measurements In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated. Volume in the graduated cylinder _____ ml

Metric Ruler Sig Figs On a metric ruler, the smallest divisions are millimeters, 0. 1 cm or 0. 001 m. Rarely does the object end neatly on one of the lines of the instrument, but that forces the use of measurement zeros. 13. 30 cm To indicate that the object being measured ends exactly at the third line after the 13, we must write 13. 30 cm. This indicates that, to our best estimation, the measurement does not extend into the hundredth of the centimeter.

Metric ruler sig figs A. B. C. D. 14 cm 14. 00 cm If the object ends exactly at the 14 cm line, we must add two zeros to the end.

Metric ruler sig figs A. B. C. D. E. F. G. H. I. J. 12. 3 cm 12. 37 cm 12. 80 cm 12. 84 cm 12. 85 cm 12. 86 cm 12. 87 cm 12. 8 cm 13. 86 cm 12. 85 cm Most of the time, our measurements fall between the lines and, we must make agonizing estimates about where the measurement does fall.

Thermometer Sig figs 68. 0 o. C ______ In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated. o -1. 1 ______ C

Triple beam balance sig figs A. B. C. D. E. F. G. H. I. J. 9 g 9. 04 g 9. 05 g 19. 04 g 19. 05 g 19. 06 g 19. 1 g In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated. 19. 04 g

Rules for writing and reading sig figs In order to present results with the proper precision, we need to know how many significant figures are present in each number we use in a calculation. There are four basic rules: 1. The digits 1 - 9 always count. 2. Zeroes between the digits 1 - 9 always count. 3. Zeroes in the beginning of a number never count. 4. Zeroes at the end of a number count only if there is a written decimal point.

Rules for writing and reading sig figs 1. 2. 3. 4. The digits 1 - 9 always count. Zeroes between the digits 1 - 9 always count. Zeroes in the beginning of a number never count. Zeroes at the end of a number count only if there is a written decimal point. Rule #1 examples: 24. 7 cm, 0. 743 cm, 714 cm All have three sig figs

Rules for writing and reading sig figs 1. 2. 3. 4. The digits 1 - 9 always count. Zeroes between the digits 1 - 9 always count. Zeroes in the beginning of a number never count. Zeroes at the end of a number count only if there is a written decimal point. Rule #2 Examples: 7003 cm, 40. 79 cm, 1. 503 cm all have 4 sig figs

Rules for writing and reading sig figs 1. 2. 3. 4. The digits 1 - 9 always count. Zeroes between the digits 1 - 9 always count. Zeroes in the beginning of a number never count. Zeroes at the end of a number count only if there is a written decimal point. Example: 0. 00701 cm, 0. 422 cm, 0. 00000909 cm all have 3 sig figs Hey!!! You can get rid of these place holding zeros by using scientific notation 7. 01 x 10 -3 cm 4. 22 x 10 -1 cm 9. 09 x 10 -6 cm

Rules for writing and reading sig figs 1. 2. 3. 4. The digits 1 - 9 always count. Zeroes between the digits 1 - 9 always count. Zeroes in the beginning of a number never count. Zeroes at the end of a number count only if there is a written decimal point. Rule 4 Examples: 43. 00 cm, 1. 010 mm, 9. 000 mm All have 4 sig figs Tricky Rule 4 Examples: the zeros in 300 cm, 7000 km and 210 m are not significant Ambiguity (doubt, uncertainty) about precision can be avoided by using scientific notation 3. 00 x 102 cm 7. 000 x 103 km 2. 1 x 102 m

Rules for writing and reading sig figs Two situations have unlimited sig figs a) counting example: there are 28 desks in the classroom b) defined quantities example: 60 minutes = 1 hour 1000 grams = 1 kilogram 7 days = 1 week

Enter answers in your notes too!! 1. Sig figs in 31. 45 m. L ? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited 31. 45 m. L Rule 1: The digits 1 - 9 always count.

Enter answers in your notes too!! 2. Sig figs in 150. 53 g ? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited 150. 53 m. L Rule 2: Zeroes between the digits 1 - 9 always count.

Enter answers in your notes too!! 3. Sig figs in 40. 00 m. L ? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited 40. 00 m. L Rule 4: Zeroes at the end of a number (trailing zeros) count only if there is a written decimal point. Has NOTHING to do with where the decimal is located !!!

Enter answers in your notes too!! 4. Sig figs in 0. 056 m. L ? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited 0. 056 m. L Rule 3: Zeroes in the beginning of a number never count. i. e. leading zeros do not count

Enter answers in your notes too!! 5. Sig figs in 10. 10 g ? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited

Enter answers in your notes too!! 6. Sig figs in 1. 5 L ? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited

Enter answers in your notes too!! 7. Sig figs in 8 yard TD pass? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited

Enter answers in your notes too!! 8. Sig figs in 220 miles to Dallas A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited 220 miles Rule 4: Zeroes at the end of a number (trailing zeros) count only if there is a written decimal point. Has NOTHING to do with where the decimal is located !!!

Enter answers in your notes too!! 9. Sig figs in 12 donuts in a dozen? A. B. C. D. E. F. G. 0 1 2 3 4 5 unlimited There always exactly 12 in a dozen. Defined quantities and counting items have unlimited sig figs.

Practice 31. 45 m. L has 4 sig figs 150. 53 g has 5 sig figs 40. 00 m. L has 4 sig figs 0. 056 seconds has 2 sig figs 10. 10 g has 4 sig figs 1. 5 L has 2 sig figs 8 yard touchdown pass has 1 sig fig 220 miles to Dallas has 2 sig figs 12 donuts in a dozen has unlisig figs

Practice 31. 45 m. L has 4 sig figs 150. 53 g has 5 sig figs 40. 00 m. L has 4 sig figs 0. 056 seconds has 2 sig figs 10. 10 g has 4 sig figs 1. 5 L has 2 sig figs 8 yard touchdown pass has 1 sig fig 220 miles to Dallas has 2 sig figs 12 donuts in a dozen has unlimited sig figs

Significant Figures in Calculations Multiplication and Division round to the same number of significant figures as the measurement with the least number of significant figures 8. 4 meters has two significant figures 2. 4526 meters ÷ 8. 4 meters 0. 29197619 meter = 0. 29 meter or 2. 9× 10 -1 meter An answer cannot be more precise than the least precise measurement from which it was calculated.

Significant Figures in Calculations � Addition and Subtraction Convert numbers to same exponent and align the decimal points, then � Round to the same number of decimal places as the least number of decimal places. � 12. 52 349. 0 + 8. 241 369. 761 meters 349. 0 meters has the least number of digits (one) to the right of the decimal point. Thus the answer must be rounded to one digit after the decimal point. The correct rounded answer is 369. 8 meters or 3. 698 X 102 meters

Significant Figures in Calculations 16 feet What is the calculated area of your college dorm room to the correct number of significant figures? 11 feet � An answer cannot be more precise than the least precise measurement from which it was calculated. � Once you know the number of significant figures your answer should have, you must round to that many digits, counting from the left.

Professor Harris reports his results to the correct number of sig figs.

Practice: 1. 5. 263 L + 9. 4 L 2. 20 s - 4. 52 s 3. 120 g X 7. 000 m. L 4. 1. 20 x 102 g X 8. 000 m. L 5. 1000. 0 g / 3. 12 L 6. 1000 g / 3. 12 L

Practice: answers with sigfigs underlined 1. 5. 263 L + 9. 4 L = 14. 663 = 14. 7 L 2 2. 20 s - 4. 52 s = 15. 48 s = 15 s 3. 120 g X 7. 000 m. L = 840 = 8. 4 x 102 gm. L 4. 1. 20 x 102 g X 8. 000 m. L = 960. gm. L or 9. 60 x 102 gm. L 5. 1000. 0 g / 3. 12 L = 320. 5128 = 321 or 3. 21 x 102 g/L 6. 1000 g / 3. 12 L = 320. 5128 = 300 or 3 x 102 g/L

Another interesting defined quantity The speed of light (usually denoted c) is a physical constant. For much of human history, it was not known whether light was transmitted instantaneously or simply very quickly. Its value is now defined to be exactly 299, 792, 458 meters per second. It has unlimited sigfigs!! 299, 792, 458. 00000000000000……. … 2. 99792458 x 108 in scientific notation How did they do that? In 1983, the meter was redefined in the International System of Units (SI) as the distance traveled by light in vacuum in 1⁄ 299, 792, 458 of a second. As a result, the value of c in meters per second is now fixed exactly by the definition of the meter.