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Introduction to Scientific Notation & Significant Figures

Introduction to Scientific Notation & Significant Figures. Packet #6. Introduction. A measurement is a quantity that has both a unit and number Measurements are fundamental to the experimental sciences. Measurements, in science, utilize the International System of Measurements (SI).

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Introduction to Scientific Notation & Significant Figures

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  1. Introduction to Scientific Notation & Significant Figures Packet #6

  2. Introduction • A measurement is a quantity that has both a unit and number • Measurements are fundamental to the experimental sciences. • Measurements, in science, utilize the International System of Measurements (SI).

  3. Scientific Notation

  4. Scientific Notation • A given number is written as the product of two numbers • A coefficient and 10 raised to a power.

  5. Converting to Scientific Notation • Positive • Decimal point goes left • Negative • Decimal point goes right

  6. Addition & Subtraction

  7. Multiplication & Division

  8. Multiplication Table

  9. Accuracy, Precision & Error

  10. Accuracy, Precision & Error • Accuracy • Measure of how close a measurement comes to the actual or true value of what ever is being measured. • Measure value is compared to correct value. • Precision • Is a measure of how close a series of measurements are to one another. • Two or more measurements are compared.

  11. Accuracy, Precision & Error • Error • Experimental value – accepted value • Experimental value • Value measure inside laboratory • Accepted Value • Correct value based on reliable references • Percent Error • Absolute value of the errordivided by accepted value, multiplied by 100 • Percent Error = • |Error|/AcceptedValue * 100

  12. Significant Figures

  13. Significant Figures • Each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit. • The significant figures in a measurement include all of the digits that are known , plus a last digit that is estimated.

  14. Significant FiguresRule #1 • Every nonzero digit in a reported measurement is assumed to be significant. • 24.7 m • 0.743 m • 714 m • All three have three significant figures

  15. Significant FiguresRule #2 • Zeros appearing between nonzero digits are significant. • 7003 m • 40.79 m • 1.503 m • All have four significant figures

  16. Significant FiguresRule #3 • Leftmost zeros appearing in front of nonzero digits are not significant. • 0.0071 m • 0.42 m • 0.000099 m • All have two significant figures • This issue is eliminated when writing in scientific notation. • 0.0071 = 7.1 * 10-3 • 0.000099 = 9.9 * 10-5

  17. Significant FiguresRule #4 • Zeros at the end of a number and to the right of a decimal point are always significant. • 43.00 m • 1.101 m • 9.000 m • All have four significant figures

  18. Significant FiguresRule #5 • Zeros are the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as place holders to show the magnitude of the number. • 300 m • 7000 m • 27210 m • The zeros in these numbers are NOT significant • One significant figure • One significant figure • Four significant figures • If the zeros were KNOWN MEASURED VALUES, then they would be significant. • Writing 300 m in scientific notation, 3.00*102 makes it clear that the zeros are significant.

  19. Significant FiguresRule #6 • There are two situations in which numbers have an unlimited number of significant figures. • Counting • If one counts 23 students in a classroom, then there are EXACTLY 23 students. • This value has an unlimited number of significant figures • Defined quantities within a system of measurement • 60 mins = 1 hr • 100 cm = 1 m • Each of these numbers has an unlimited number of significant figures. • However, exact quantities do not affect the process of rounding an answer to the correct number of significant numbers.

  20. Significant FiguresProblems • How many significant figures are in each measurement and what ultimate rule applies? • 123 m • 40506 mm • 9.8000*104 • 22 meter sticks • 0.07080 m • 98000 m

  21. Significant FiguresProblems II • 314.721 meters (four) • 0.001775 meters (two) • 8792 meters (two)

  22. Addition & Subtraction Significant Figures

  23. Addition & Subtraction Rule • The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

  24. Addition & Subtraction • Calculate the sum of the three measurements. Give the answer to the correct number of significant figures. • 12.52 meters + 349.0 meters + 8.24 meters • Solving the problem • Calculate the sum and then analyze each measurement to determine the number of decimal places required in the answer.

  25. Addition & Subtraction II • Align the numbers based upon what is provided. • Final answer should be 369.76 meters. • The second measurement, 349.0 meters, has the least number of digits after the decimal point. • The answer is rounded to 369.8 meters or 3.698 * 102 meters.

  26. Multiplication & Division Significant Figures

  27. Multiplication & Division Rule • In calculations involving multiplication and division, one needs to round the answer to the same number of significant figures as the measurement with the least number of significant figures.

  28. Examples • 7.55 meters * 0.34 meters • 2.10 meters * 0.70 meters • 2.4526 meters ÷ 8.4

  29. Review

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