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Significant Figures and Scientific Notation

Significant Figures and Scientific Notation. Chemistry Pre-teach. Significant Figures. The significant figures of a number are those digits that carry meaning in its precision . Precision How well a value can be reproduced through repeated measurement. Accuracy

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Significant Figures and Scientific Notation

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  1. Significant Figures and Scientific Notation Chemistry Pre-teach

  2. Significant Figures • The significant figures of a number are those digits that carry meaning in its precision. • Precision • How well a value can be reproduced through repeated measurement. • Accuracy • How close a measurement comes to the actual (true) value.

  3. Accuracy vs. Precision

  4. WHY? What is the measurement for each of these graduated cylinders? 1.0 mL 0.1 mL 52.5 mL 6.60 mL The last digit is an estimation based on the position of the meniscus.

  5. Precision • Precision of a measurement relies on the design of the measuring device. To what accuracy is the graduated cylinder? Could you use this to measure 8.423 mL? Could you use this to measure 45.0 mL?

  6. Significant Figure Rules • Any non-zero number (1-9). • Some zeros are significant: • Zeros at the front of a number are not significant • Zeros in the middle of significant numbers are always significant • Zeros at the end are significant if there is a decimal. Examples: 534 0.034 1003.5 1.00 1000. 3 significant figures 2 sig figs 5 sig figs 3 sig figs 4 sig figs

  7. Practice • How many significant figures do each of these values contain? • 2.5 in • 404 cm • 0.02 m • 0.203 mL • 0.0020500 L • 500. miles • 0.100 torr • 0010 gallons • 62,043.050800 m/s • 0.00000100100 m

  8. Sig Figs of Addition and Subtraction • Add or subtract the numbers as normal. • Determine the value that has the least number of significant decimal places. • Round to figure in that decimal place. • Ex. 102.15 + 105.2 207.35 hundreds place 3400 + 2534.03 5934.03 Tenths place 5900 207.4

  9. Sig Figs of Multiplication and Division • To determine significant figures after multiplying or dividing • Multiply or divide as normal. • Find the given value with the least number of sig figs. • Round the answer to that number of sig figs. • Ex: 521 x 31 = 16,151 3 2 Round down to 2 sig figs 16,000

  10. Examples • 23.87 + 12.3 = ? • 23.87 x 12.3 = ?

  11. Scientific Notation • A convenient method to write very large or very small numbers. • 6.63 x 10-34 = 0.000000000000000000000000000000000663 • 6.02 x 1023 = 602000000000000000000000

  12. Scientific Notation • Determine the number of significant figures. • Move the decimal so that there is only one nonzero digit (1-9) in front of the decimal. • Record the value as a decimal with the number of significant figures. • Record the movement of the decimal as the exponent in 10x.

  13. Scientific Notation • Decimal movement: • Move left => positive exponent • Move right => negative exponent • To get back to standard notation, reverse the movement of the decimal. Ex. 1013.0 = 1.0130 x 103 0.0000456 = 4.56 x 10-5

  14. Convert from standard notation to scientific notation: • -0.004770 • 35,600,000 • 342.79 • Convert from scientific notation to standard notation: • 4.56 x 103 • -1.75 x 10-5 • 6.3 x 101

  15. Metric Prefixes • gigaG 109 • mega M 106 • kilo k 103 • hecto h 102 • deca da 101 • deci d 10-1 • centi c 10-2 • milli m 10-3 • micro μ 10-6 • nano n 10-9 • pico p 10-12 • femto f 10-15

  16. Examples 3,980 m = 3.98 x 103 m= 3.98 km 0.0246 L = 24.6 x 10-3 L= 24.6 mL 9,000,000 Hz = 9 x 106 Hz = 9 MHz 1.34 x 10-14 s = 13.4 x 10-15 s = 13.4 fs

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