SIGNIFICANT FIGURES SIGNIFICANT FIGURES Significant Figures Sig Figs

SIGNIFICANT FIGURES

SIGNIFICANT FIGURES Significant Figures ( Sig. Figs) Measured digits in a reported number. More Sig. Figs = more confidence Less Sig. Figs = less confidence A Laboratory instrument is read as far it can be, and the last number is estimated. There are Limitations to how confident you can be! Compare 2 m vs. Which one seems more confident? 2. 00 m

What is the correct mass to report? Measured Mass is ________

What is the correct mass to report? Measured Mass is 500 + 40 + 6. 25 g OR 546. 25 g

SIGNIFICANT FIGURES Rules for recognizing Sig. Figs: When a number has a decimal: Read Left to Right until you Reach the first nonzero number Then you begin counting Sig. Figs Until you run out of digits (including any zeros along the way) Example: 0. 003210 g = _______ Sig. Figs?

SIGNIFICANT FIGURES Practice: 82. 700 K 0. 000365 J 3. 034 g 3. 220 x 105 m ____sig figs

SIGNIFICANT FIGURES Rules for recognizing Sig. Figs: When a number has no decimal: Read Right to Left until you Reach the first nonzero number Then you begin counting Sig. Figs Until you run out of digits (including any zeros along the way) Example: 450300 m = _______ Sig. Figs?

SIGNIFICANT FIGURES Practice: 421 m 800, 890 J 39, 059, 000 g 523, 000 L ____ sig figs ____sig figs

SIGNIFICANT FIGURES Counted Quantites and Constants have absolute values & we don’t count Sig. Figs Either you counted the number of items right, or you didn’t! Example: 14 bananas

SIGNIFICANT FIGURES How many significant figures are in each of the following numbers? 1. 2. 3. 4. 5. 40 ng 1. 2 x 103 mt 210 N 0. 00120 m. L 801. 5 K ____ ____ 6. 7. 8. 9. 10. 0. 0102 Amp 1, 000 BTU 9. 010 x 10 -6 dm 101. 0100 D 2, 370. 0 Cal ____ ____

SIGNIFICANT FIGURES Why are significant figures important when taking data in the laboratory? When you measure something, you never get 100% accuracy on its measurement, so you need a way to show just how accurate it is.

SIGNIFICANT FIGURES Why are significant figures NOT important when solving problems in your math class? In math, we assume that all numbers are either 100% accurate, or that they are constants, and thus have no uncertainty or error involved in their creation.

SIGNIFICANT FIGURES Using two different instruments, I measured the length of my foot to be 27 centimeters and 27. 00 centimeters. Explain the difference between these two measurements. The second measurement was made with a ruler that had more graduations, giving a higher level of certainty and more Significant Figures

SIGNFICANT FIGURES AND MATH We will be required to do math with our Sig. Figs Two rule sets cover this: Addition/Subtraction And Multiplication/Division

ADDITION AND SUBTRACTION SIG FIG RULES line up the decimals 2. draw a line to the right of the number with the least precision (shortest column) 3. answer can’t go past the line 4. use the 1 st digit past the line to determine where to round off Example: 32. 00 m + 48. 1 m + 182. 213 m = ? ? 1.

ADDITION AND SUBTRACTION SIG FIG RULES line up the decimals 2. draw a line to the right of the number with the least precision (shortest column) 3. answer can’t go past the line 4. use the 1 st digit past the line to determine where to round off Example: 32. 00 m + 48. 1 m + 182. 213 m = ? ? 1. 32. 00 m 48. 1 m +______ 182. 213 m 262. 313 m Must round to: 262. 3 m

ADDITION AND SUBTRACTION SIG FIG RULES 1. 210. 6 mm + 14. 57 mm = ______ 2. 74. 000 cm + 8. 6 cm =______ 3. 0. 0787 m + 0. 85 m =______ 4. 84000 cm + 1110 cm =______ 5. 92008 g + 32100 g =______ 6. 8. 000 mm + 0. 0304 m =______ 7. 84. 34 g - 5. 2 g =______ 8. 9. 81 cm - 3. 151 cm =______ 9. 0. 0900 n - 0. 0094 n =______

MULTIPLYING AND DIVIDING SIG FIG RULES Answer can have no more Sig. Figs than the factor with the fewest number of Sig. Figs. This means that constants and quantities do not affect sigfigs in the answer! Example: 127. 3 x 42 = ? ? ?

MULTIPLYING AND DIVIDING SIG FIG RULES 1. 500 kg X 32 kg =______ 2. 680. 0 n X 100. n =______ 3. 8560. 0 g X 1000 g =______ 4. 4560 m X 0. 100 m =______ 5. 85 kg X 0. 001 kg =______ 6. 9200 L ÷ 873 L =______ 7. 0. 85 2 kg 2 ÷ 62 kg =______ 8. 985 g 2 ÷ 500. g =______ 9. 10000 n 2 ÷ 0. 10 n =______ 10. 0. 0006 g 2 ÷ 25 g=______