Scientific Notation Significant Figures and Metric 91014 Scientific

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Scientific Notation, Significant Figures and Metric 9/10/14

Scientific Notation, Significant Figures and Metric 9/10/14

Scientific Notation o The components of scientific notation: 8. 238 x 10 -31 o

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

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 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

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

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.

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

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

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

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

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

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

The Atlantic and Pacific Rule for Significant Figures o "P" for "Present". This means

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

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

Examples 1) 0. 020110 2) 730800 3) 3300 4) 3300. 0

Rounding Sig. Figs.

Rounding Sig. Figs.

Rounding Sig. Figs. o The goal is to round the number to the appropriate

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

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

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 =

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

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

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

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”

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

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

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

Extra Practice

Sig. Figs. Practice Ex 1) 0. 020110 Ex 2) 730800 n 1) 48001 n

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

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.

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.

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