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Chapter 3: Scientific Measurement

Chapter 3: Scientific Measurement. Scientific Notation and Significant Figures. Learning Targets. You will learn significant digits. Scientific Notation Refresher. Scientific notation is a shorthand way of writing very large or very small numbers.

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Chapter 3: Scientific Measurement

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  1. Chapter 3: Scientific Measurement Scientific Notation and Significant Figures

  2. Learning Targets • You will learn significant digits.

  3. Scientific Notation Refresher • Scientific notation is a shorthand way of writing very large or very small numbers. • These numbers are written as a number between 1 and 10 multiplied by a power of 10. • The power of 10 represents the number of places the decimal moves. • Numbers bigger than 1 have positive powers of 10. • Numbers smaller than 1 have negative powers of 10.

  4. Scientific Notation-Calculator • Enter the # b/t 1 and 10, press the EE button, enter the exponent. • This button makes it much easier and provides less room for error in the future so USE IT! • Look for a button that says EE. It might be a 2nd function button. (1 E shows up on the screen) • The EE button (1 E shows up on your screen) takes the place of x 10 ^

  5. Examples: 93,000,000 (original) 9.3 x 107 (scientific notation) 0.000167 (original) 1.67 x 10-4 (scientific notation) Notice the original numbers: > or < 1 Notice the exponents: + or – Notice the number between 1 and 10: Which way did the decimal move? L or R How many places did the decimal move? Scientific Notation

  6. 1457 (4) 0.0025 (2) 1.008 (4) 100 (1) 100. (3) 1 in. = 2.54 cm (unlimited) 3 apples, 8 molecules, 10 experiments (unlimited) Nonzero numbers ARE Zeros before nonzero numbers ARE NOT Zeros between nonzero numbers ARE Zeros to the right of any nonzero number ARE, ONLY if written with a decimal point Exact numbers (usually #’s determined by counting or conversions) ARE UNLIMITED Unlimited means the numbers in question will not limit sig figs in your final answer Significant Figures-Rules You will learn significant digits.

  7. Significant Figures-Rules • Pacific Ocean - P means PRESENT • Atlantic Ocean – A means ABSENT • It is the decimal point that is present or absent • Draw an arrow through the number and stop at the first nonzero digit • Numbers in scientific notation have the same rules applied for significant figures, just disregard the power of 10. You will learn significant digits.

  8. Give the number of significant figures for each of the following measurements: 0.0108 g 0.0050060 g 0.000304 g 0.09020 L 4.0 x 10-1 cm3 5.030 x 103 ft. 2.0800 x 102 L Answers: 3 sig figs 5 sig figs 3 sig figs 4 sig figs 2 sig figs 4 sig figs 5 sig figs Examples You will learn significant digits.

  9. Give the number of significant figures for each of the following measurements: 0.003042 1.4030 1000 0.060 50.0 10.47020 250. Answers: 4 sig figs 5 sig figs 1 sig figs 2 sig figs 3 sig figs 7 sig figs 3 sig figs Try on your own: You will learn significant digits.

  10. Significant Figures - Calculations • What methods do you use to compute answers (think math skills)? • Multiplication, Division, Addition and Subtraction • Knowing what you know about sig figs and scientific notation you can compute answers and report those number to the correct number of significant figures You will learn significant digits.

  11. Multiplication and Division DO NOT ROUND UNTIL THE END OF YOUR CALCULATIONS! The measurement with the fewest sig figs is what limits your final calculation Keep your numbers and places accounted for. 4 and below – let it go 5 and above – give it a shove Addition and Subtraction DO NOT ROUND UNTIL THE END OF YOUR CALCULATIONS! The right most column where each measurement has a number is the place you round off to. Round the same way as multiplication and division. Significant Figures-Calculations You will learn significant digits.

  12. Compute each problem to the correct amount of significant figures: 4.56 x 1.4 8.315 / 298 12.11 + 18.0 + 1.013 0.6875 – 0.1 5.0 cm + 11.28 cm 0.0120 cm x 5.350 cm (25.36 – 4.15) / 2.317 Answers: 6.4 0.0279 31.1 0.6 16.3 cm 0.0642 cm2 9.154 Examples You will learn significant digits.

  13. Compute each problem to the correct amount of significant figures: 5.18 x 0.0208 (3.60 x 10-3) x (8.123) / 4.3 21 + 13.8 + 130.3 116.8 – 0.33 (1.33 x 2.8) + 8.41 12.6 x 0.53 (12.6 x 0.53) – 4.59 Answers: 0.108 .0068 165 116.5 12.1 6.7 2.1 Try on your own You will learn significant digits.

  14. SUMMARIZE • How do you write a number in scientific notation? • What is a significant number? • How do you know what is one? • What is an uncertain number? • How do you round off in calculations?

  15. Homework • Page 95: 57-60 You will learn significant digits.

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