Scientific Notation Significant Figures and Metric 91014 Scientific
- Slides: 32
Scientific Notation, Significant Figures and Metric 9/10/14
Scientific Notation o The components of scientific notation: 8. 238 x 10 -31 o “ 8. 238” is the coefficient o “x 10” is the base o “-31” is the exponent o Where the coefficient has to be a number: 1 ≤ coefficient < 10
Significant Figures o Significant Figures (sig. figs. ): the number of digits that carry meaning contributing to the precision of a measurement or calculated data.
Precision and Accuracy Low Accuracy High Precision High Accuracy Low Precision High Accuracy High Precision
Significant Figures o Each recorded measurement has a certain number of significant figures. o Calculations done on these measurements must follow the rules for significant figures. o Placeholders, or digits that have not been measured or estimated, are not considered significant.
Significant Figures o There are 5 rules to determine which zeros in a number are significant or not.
Rules for Significant Figures o Rule #1: All non-zero digits (1 -9) are significant. For example: 453 number of sig figs______ 345. 21 number of sig figs______
Rules for Significant Figures o Rule #2: Zeroes between non-zero digits are significant. For example: 12. 007 number of sig figs______ 2014 number of sig figs______
Rules for Significant Figures o Rule #3: If a number ends in zeroes, the zeroes to the right are NOT significant IF there is NO decimal point present. For example: 47100 number of sig figs______ 20060 number of sig figs______ 40000 number of sig figs______
Rules for Significant Figures o Rule #4: Zeroes to the left of the first non- zero digit are NOT significant. For example: 1. 02 0. 12 0. 00127 0. 00040301 number of sig figs______ number of sig figs______
Rules for Significant Figures o Rule #5: If a number ends in zeroes to the right of the decimal point, those zeroes are significant. For example: o 2 number of sig figs______ 2. 0 number of sig figs______ 2. 00 number of sig figs______ 2. 000 number of sig figs______ {This signifies greater precision. }
The Atlantic - Pacific Rule for Significant Figures o When determining the number of significant figures ask the question: o “Does the number have a decimal point? ” (YES or NO answer) o If YES, then think of “P” for Present and the Pacific ocean o If NO, then think of “A” for Absent and the Atlantic ocean
The Atlantic and Pacific Rule for Significant Figures
The Atlantic and Pacific Rule for Significant Figures o "P" for "Present". This means that we imagine an arrow coming in from the Pacific ocean, from the left side o "A" for "Absent". This means that we imagine an arrow coming in from the Atlantic ocean, the right side.
The Atlantic and Pacific Rule for Significant Figures o Look for the first non zero number starting from that direction o That number, and all other numbers following it are considered to be significant n For “P” the numbers to the right of the first non zero number n For “A” the numbers to the left of the first non zero number
Examples 1) 0. 020110 2) 730800 3) 3300 4) 3300. 0
Rounding Sig. Figs.
Rounding Sig. Figs. o The goal is to round the number to the appropriate amount of sig. figs. without changing the value too much.
Rounding Calculations o For multiplication and division: o Round to the number that has the least amount of sig. figs. o Note: There are different rules for addition and subtractions
Rounding Sig. Figs. o Look at the left most non-zero numbers to identify the ones that you will keep o If the number to the right of the last digit is 5 or higher round up, 4 or lower round down n LEFT of Decimal: Replace non significant figures with zeroes if they are to the LEFT of the decimal point n RIGHT of Decimal: Drop non significant figures if they are to the RIGHT of the decimal point
Examples in Your Notes o 1) 43252202 to 3 sig figs 43252202 (5 = 5 so round up and replace non sig. figs. with zeros) o 43300000 o 2) 0. 0073384658419 to 4 sig figs o 0. 0073384658419 (4 < 5 so round down and drop non sig. figs. ) o 0. 007338 o
Examples in Your Notes o 3) 47. 66666667 to 5 sig figs 47. 66666667 (6 > 5 so round up and drop non sig. figs. ) o 47. 667 o 4) 794951. 741583 to 2 sig figs o 794951. 741583 (4 < 5 so round down and replace non sig. figs. with zeroes AND drop non sig. figs. to the right of the decimal) o 790000 o
Rounding Calculations Examples 1. 5. 50 × 2. 00 2. 2. 437 × 10 -12 / 4. 5 × 1014
Rounding Calculations Examples 1. 5. 50 × 2. 00 Calculator reads “ 11” Answer is 11. 0 2. 2. 437 × 10 -12 / 4. 5 × 1014 Calculator reads “ 5. 415555556 E-27” Answer is 5. 4 × 10 -27
Lab Rubric o 1 st column “Self Evaluation” o 2 nd column “Peer Evaluation” (student initials) o 3 rd column “Self Evaluation #2” o 4 th column “Teacher Evaluation”
Metric Units (base unit) Quantity Base Unit Symbol Length Meter m Mass Gram g Time Second s Volume Liter L Force Newton N Energy Joule J
Metric Prefixes *Learn highlighted ones! Prefix Symbol Multiplier mega- M 106 (1000000) kilo- k 103 (1000) BASE UNIT - 100 (1) centi- c 10 -2 (0. 01) milli- m 10 -3 (0. 001) micro- μ 10 -6 (0. 000001)
Extra Practice
Sig. Figs. Practice Ex 1) 0. 020110 Ex 2) 730800 n 1) 48001 n 2) 9807000 n 3) 0. 008401 n 4) 40. 500 n 5) 64000 n 6) 64000. n 7) 64000. 00 n 8) 0. 0107050
Sig. Figs. Practice Ex 1) 0. 020110 Ex 2) 730800 n 1) 48001 n 2) 9807000 n 3) 0. 008401 n 4) 40. 500 n 5) 64000 n 6) 64000. n 7) 64000. 00 n 8) 0. 0107050 Ex 1) 0. 020110 (5 sig. figs. ) Ex 2) 730800 (4 sig. figs) n 1) 48001 (5 sig. figs. ) n 2) 9807000 (4 sig. figs. ) n 3) 0. 008401 (4 sig. figs. ) n 4) 40. 500 (5 sig. figs. ) n 5) 64000 (2 sig. figs. ) n 6) 64000. (5 sig. figs. ) n 7) 64000. 00 (7 sig. figs. ) n 8) 0. 0107050 (6 sig. figs. )
Rounding Practice 1. 0. 0018563333 to 3 sig. 2. 3. 4. 5. 6. 7. 8. figs. 34498221 to 2 sig. figs. 4781. 2233 to 3 sig figs. 568. 7893201 to 5 sig. figs. 67488133 to 1 sig. fig. 0. 0219999 to 2 sig. figs. 4. 7004021 to 4 sig. figs. 998701 to 1 sig. fig.
Rounding Practice 1. 0. 0018563333 to 3 sig. 2. 3. 4. 5. 6. 7. 8. figs. 34498221 to 2 sig. figs. 4781. 2233 to 3 sig figs. 568. 7893201 to 5 sig. figs. 67488133 to 1 sig. fig. 0. 0219999 to 2 sig. figs. 4. 7004021 to 4 sig. figs. 998701 to 1 sig. fig. 1. 0. 00186 2. 34000000 3. 4780 4. 568. 79 5. 70000000 6. 0. 022 7. 4. 700 8. 1000000
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