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Scientific Measurements

Scientific Measurements. Objective I. Convert measurements to scientific notation. As a group, list as many measurements you can. Scientific Notation. exponential form a number is written as the product of 2 numbers a coefficient and 10 raised to a power 3.2 x 10 9.

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Scientific Measurements

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  1. Scientific Measurements Objective I. Convert measurements to scientific notation As a group, list as many measurements you can.

  2. Scientific Notation exponential form • a number is written as the product of 2 numbers a coefficient and 10 raised to a power 3.2 x 109

  3. Coefficient  is always a number greater than or equal to one and less than 10 • The exponent indicates how many times the coefficient must be multiplied by 10 to equal the standard number Ex: 8.4 x 104 = 8.4 x 10 x 10 x 10 x 10 = 84,000

  4. Writing numbers greater than 10 in scientific notation Move the decimal all the way to the left until you only have one number on the left side of the decimal. ex: 6,000,000 6.000000 Count how many places you moved the decimal 6 You will write the whole number, decimal, 1 zero 6.0 Next, you will place an x (times), then the base 10 with an exponent. The exponent will be the number of spaces you moved the decimal. 6.0 x 106

  5. Practice = 6.2 x 104 = 3.45 x 108 = 8.7 x 1010 = 6.452 x 103 62,000 345,000,000 87,000,00000 6452

  6. What if the number is not a whole number (number less than 10 to start with? • These numbers will be written with a negative exponent. • You will move the decimal to the right this time. Still count the places you moved. You will also still have 1 whole number on the left of the decimal. • Ex: .00000000458 • 000000004.58 • Count how many places you moved the decimal • 9 • Drop the numbers before the 4 (they are not significant) • 4.58 • Now write this number with your base 10 and exponent • 4.58 x 10-9

  7. REMEMBER!!!! • If you move decimal , the exponent will be negative • If you move decimal , the exponent will be positive

  8. More practice • 98,090,000 • 789000 • .0098 • .000008 = 9.809 x 107 = 7.89 x 105 = 9.8 x 10-3 = 8 x 10-6

  9. Scientific notation to standard form • 8.3 x 104 Move the decimal 4 places to the right. 8.3 x 10-4 Move the decimal 4 places to the left • Try these! • 2.0 x 105 200,000 • 5.6 x 10-4 .00056

  10. Accuracy vs Precision • Measurements should be both correct and reproducible. • Quite different • Accuracy- how close a measurement comes to the actual or true value of whatever is measured. • Precision- how close a series of measurements are to one another.

  11. A B B C

  12. ERROR??? • Water boils at 100oC • LAB= WATER BOILED AT 99.10C • WHAT HAPPENED? • ERROR = EXPERIMENTAL VALUE – ACCEPTED VALUE • Percent error=IerrorI X 100% Accepted value % error= I99.1 – 100.0I x 100% 100.0 = 0.9/100.0 x 100% = 0.009 x 100% = 0.9%

  13. THINK!!! • If you look back at almanacs, olympic track records were recorded differently. • From 1948 to 1999 they were recorded to the nearest tenth (9.5), but since 2000 they are recorded to the nearest hundredth (9.49) • Why do you think more recently recorded race times contain more digits to the right of the decimal?

  14. Significant Numbers (digits) Include all digits know plus last estimated digit.

  15. Calculating with Significant digits • A calculated answer cannot be more precise than the least precise measurement from which it was calculated • Don’t round your answers until you figure out the number of significant digits to use • Round to the correct # of significant numbers, then apply rules for expressing number in scientific notation.

  16. Practice pg 69

  17. Significant figures in addition ADD: 12.52 349.0 + 8.24 __________ 369.76= 369.8 or 3.698 x 102 • Align the decimal points and add the numbers • Round the answer to match the measurement with the least number of decimal places. • 349.0 has the least sig. fig. to the right (1). So, we must round out answer to one place past decimal

  18. Practice 61.2 + 9.35 + 8.6 = 9.44 – 2.11 = 34.61 - 17.3

  19. Multiplication & Division • Round the answer the the same number of significant numbers as the measurement with the least number of significant digits. • Ex: 7.55 x 0.34 = 2.567 • 0.34 only has 2 sig. fig. so we round our answer so it only has 2. • 2.567 = 2.6

  20. a) 2.10 x 0.70 =b) 2.4526 / 8.4 =c) 8.3 x 2.22 =d) 8432 / 12.5 =e) 22.4 m x 11.3 m x 5.2 m =

  21. Quick lab P. 72

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