Scientific Notation, Significant Figures and Metric

9/10/14

Scientific Notation

The components of scientific notation:8.238 x 10-31

“8.238” is the coefficient “x 10” is the base “-31” is the exponent Where the coefficient has to be a number:

1 ≤ coefficient < 10

Significant Figures

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 AccuracyHigh Precision

High AccuracyLow Precision

High AccuracyHigh Precision

Significant Figures

Each recorded measurement has a certain number of significant figures.

Calculations done on these measurements must follow the rules for significant figures.

Placeholders, or digits that have not been measured or estimated, are not considered significant.

Significant Figures

There are 5 rules to determine which zeros in a number are significant or not.

Rules for Significant Figures

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

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

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______ 40000number of sig figs______

Rules for Significant Figures

Rule #4: Zeroes to the left of the first non-zero digit are NOT significant.

For example:1.02 number of sig figs______0.12 number of sig figs______0.00127 number of sig figs______ 0.00040301 number of sig figs______

Rules for Significant Figures

Rule #5: If a number ends in zeroes to the right of the decimal point, those zeroes are significant.For example:

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

When determining the number of significant figures ask the question:

“Does the number have a decimal point?” (YES or NO answer)

If YES, then think of “P” for Present and the Pacific ocean

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

"P" for "Present".  This means that we imagine an arrow coming in from the Pacific ocean, from the left side

"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

Look for the first non zero number starting from that direction

That number, and all other numbers following it are considered to be significant For “P” the numbers to the right of the first

non zero number For “A” the numbers to the left of the first

non zero number

Examples

1) 0.0201102) 7308003) 33004) 3300.0

Rounding Sig. Figs.

Rounding Sig. Figs.

The goal is to round the number to the appropriate amount of sig. figs. without changing the value too much.

Rounding Calculations

For multiplication and division: Round to the number that has the least

amount of sig. figs. Note: There are different rules for addition

and subtractions

Rounding Sig. Figs. Look at the left most non-zero numbers to identify

the ones that you will keep If the number to the right of the last digit is 5 or

higher round up, 4 or lower round down LEFT of Decimal: Replace non significant

figures with zeroes if they are to the LEFT of the decimal point

RIGHT of Decimal: Drop non significant figures if they are to the RIGHT of the decimal point

Examples in Your Notes

1) 43252202 to 3 sig figs 43252202 (5 = 5 so round up and replace

non sig. figs. with zeros) 43300000 2) 0.0073384658419 to 4 sig figs 0.0073384658419 (4 < 5 so round down and

drop non sig. figs.) 0.007338

Examples in Your Notes

3) 47.66666667 to 5 sig figs 47.66666667 (6 > 5 so round up and drop non

sig. figs.) 47.667 4) 794951.741583 to 2 sig figs 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)

790000

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 “5.415555556E-27”

Answer is 5.4 × 10-27

Lab Rubric

1st column “Self Evaluation” 2nd column “Peer Evaluation” (student initials) 3rd column “Self Evaluation #2” 4th 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 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) 0.020110Ex 2) 730800

1) 48001 2) 9807000 3) 0.008401 4) 40.500 5) 64000 6) 64000. 7) 64000.00 8) 0.0107050

Sig. Figs. Practice

Ex 1) 0.020110Ex 2) 730800

1) 48001 2) 9807000 3) 0.008401 4) 40.500 5) 64000 6) 64000. 7) 64000.00 8) 0.0107050

Ex 1) 0.020110 (5 sig. figs.)Ex 2) 730800 (4 sig. figs)

1) 48001 (5 sig. figs.) 2) 9807000 (4 sig. figs.) 3) 0.008401 (4 sig. figs.) 4) 40.500 (5 sig. figs.) 5) 64000 (2 sig. figs.) 6) 64000. (5 sig. figs.) 7) 64000.00 (7 sig. figs.) 8) 0.0107050 (6 sig. figs.)

Rounding Practice

1. 0.0018563333 to 3 sig. figs.

2. 34498221 to 2 sig. figs.

3. 4781.2233 to 3 sig figs.

4. 568.7893201 to 5 sig. figs.

5. 67488133 to 1 sig. fig.

6. 0.0219999 to 2 sig. figs.

7. 4.7004021 to 4 sig. figs.

8. 998701 to 1 sig. fig.

Rounding Practice

1. 0.0018563333 to 3 sig. figs.

2. 34498221 to 2 sig. figs.

3. 4781.2233 to 3 sig figs.

4. 568.7893201 to 5 sig. figs.

5. 67488133 to 1 sig. fig.

6. 0.0219999 to 2 sig. figs.

7. 4.7004021 to 4 sig. figs.

8. 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