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Significant Figures

Learn about significant figures, accuracy, precision, and how to perform math operations with significant figures and scientific notation.

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Significant Figures

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  1. Significant Figures Aren’t all numbers important?!?!?!? Yes, but some are more significant than others…

  2. Accuracy / Precision • Accuracy – the agreement between a measured value and a true value. • Precision – agreement between several measurements of the same quantity.

  3. Significant Figures • A measurement can only be as accurate and precise as the instrument that produced it. • A scientist must be able to express the accuracy of a number, not just its numerical value

  4. Significant Figures • We can determine the accuracy of a number by the number of significant figures it contains.

  5. Doing Math with Sig. Figs. ADDING AND SUBTRACTING: If you add two numbers together the answer is only as precise as your least precise number. Your answer will have only as many digits after the decimal point as your least Precise number. Example: 5.46 + 2.0 + 3.1111 = 10. 571 The 2.0 has only 1 significant figure past the decimal, so our answer can only have 1 digit pas the decimal. Answer = 10.6

  6. Multiplication and Division with Sig. Figs. Your answer can only be as precise as your least precise number. This time we are not just worried about after the decimal, but the least precise number as a whole. You answer should have the same number of significant figures as the number In the problem with the fewest significant figures. Example: (3.78 x 4.0001 x 4.5) = 68.041701 The 4.5 only has two significant figures so our answer can only have two. Answer = 68

  7. Scientific Notation Helping us write really tiny or really bignumbers

  8. Carelessness when using numbers • I have a million math problems to do • I have a trillion things to get done tonight • If you win 1 million dollars and you’re given the prize in 100 dollar bills, your stack of money is…. 4 inches high

  9. Rules to Scientific Notation Parts: 1. Coefficient (mantissa) – must be a number from 1 – 9.9 2. Exponent – a power of 10 3.4 x 106 Easier than writing 3,400,000

  10. Numbers Greater Than 10 • Find the number by moving the decimal point that is between 1 – 9.9 45,300,000  4.53 • Write a positive exponent which is equal to the number of places you moved the decimal point to the left. 4.53 x 107

  11. Numbers Less Than 1 • Find the number by moving the decimal point that is between 1 – 9.9 0.000291  2.91 • Write a negative exponent which is equal to the number of places you moved the decimal point to the right. 2.91 x 10-4

  12. Math Operations & Sci. Notation • For Multiplication: multiply coefficients add exponents (3.0 x 104) x (2.0 x 102) = 6.0 x 106 3 x 2 = 6 4 + 2 = 6

  13. Math Operations & Sci. Notation • For Division: divide coefficients subtract exponents (6.4 x 106) / (1.7 x 102) = 3.8 x 104 6.4 / 1.7 = 3.8 6 – 2 = 4

  14. Be Careful… • Remember the rule about the coefficient! Ex. (4.0 x 103) x (3.0 x 104) = 12.0 x 107 WRONG!!! Answer = 1.2 x 108

  15. Math Operations & Sci. Notation • For Addition and Subtraction: must make the exponents the same Ex. 5.4 x 103 + 6.0 x 104 = 0.54 x 104 +6.0 x 104 6.5 x 104

  16. Special Note • Sometimes exponents are written differently. • We are used to 3.4 x 105 • However, you may see 3.4E5 • It means the same thing (“E” represents the exponent and replaces x 10

  17. 0.02 _____ 0.020 _____ 501 _____ 501.0 _____ 5,000 _____ 5,000. _____ 6,051.00 _____ 0.0005 _____ 0.1020 _____ 10,001 _____ 8040 ______ 0.0300 ______ 699.5 ______ 2.000 x 102 ______ 0.90100 ______ 90,100 ______ 4.7 x 10-8 ______ 10,800,000. ______ 3.01 x 1021 ______ 0.000410 ______ Write in Scientific Notation and Determine the number of sig. figs.

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