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Units of Measurement

This guide explores the fundamentals of measurement, scientific notation, and significant figures, essential concepts in science. We cover how to measure large and small quantities using the mole and how to express these measurements in scientific notation. You'll learn how to convert between decimal and scientific notation and the rules governing significant figures to ensure accuracy in your calculations. Practical examples and exercises are provided to reinforce understanding and application of these concepts in real-world scenarios.

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Units of Measurement

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  1. Units of Measurement We measure everything! see table 1.1 and 1.2

  2. Examples of Measurements will we use numbers that big/small in class? yep! the mole

  3. the mole 602,213,700,000,000,000,000,000 particles or 6.022137 x 10 23 particles scientific notation!

  4. Scientific Notationa way to write really big numbers

  5. How to go to sci. notation Numbers bigger than ten will have positive exponents that will equal how many times decimal moved to the left 36000 = 3.6 x 104 Numbers smaller than ten will have a negative exponents that will equal how many times it moved to the right 0.0081 = 8.1 x 10-3

  6. Practice Write in scientific notation • 914 m • 0.000 000 000 154 g 9.14 x 102m 1.54 x 10-10g

  7. How to go from sci. notation Positive exponent = decimal moves to right 8.25 X 104= 82500 Negative exponent = decimal moves to left 1.2 X 10 -3= .0012

  8. Practice Write in scientific notation • 2.157 X 10 5 L • 6.5 X 10-2 m 215 700 L .065 m

  9. ?’S

  10. which measurement is best? • 1200g • 1.200 x 103g • 1.2 x 103g

  11. Significant Figures= digits recorded in measuring the more sig figs the greater the certainty

  12. Rules • All nonzeroes are significant • Zeroes in-between are significant • Zeroes to the left are not significant • Zeroes to the right are not significant unless they follow a decimal. • All numbers in scientific notation are significant • Exact numbers are obtained by counting or definitions such as 1 in = 2.54 cm, and are considered infinite in significance

  13. Practice How many sig figs are in the following? • 0.0950 m • 9009.0 J • 10 km • 60 sec = 1min • 5.50 x 108ng 3 5 1 infinite! 3

  14. so…which measurement is best? • 1200g • 1.200 x 103g • 1.2 x 103g

  15. Adding and Subtracting Always use the least significant decimal place. example: 1253.747 + 1.1 = 1254.8 = 1254.9 round up 1253.757 + 1.1 .0365578 - .00223 = .03433 or 3.433 X 10-2

  16. Practice complete the following • 8.7 g + 15.43 g + 19 g = • 853.2 L - 627.443 L = • 5.47 m + 11.0 m + 87.300 m = 43 g 225.8 L 103.8 m

  17. Multiplying and Dividing All ways go by the least number of significant figures. examples: 1253.747 X 1.1 = 1379.1217 No 1400 or 1.4 x 103

  18. Practice complete the following • 4.32 cm x 1.7 cm = • 38.742kg ÷ 0.421 = • 5.40 m x 3.21 m x 1.871 m = 7.3 cm2 92.0 kg 32.4 m3

  19. Combining the math • Follow order of operations • 55.657 -55.654 X .033 = 4.54 • 0.003 X .033 = 2 x 10-5 (1 sig fig) 4.54

  20. Practice 8.52 + 4.1586  18.73 + 153.2 = 239.6 or 2.396 x 102 = 8.52 + 77.89 + 153.2 = 239.61 =

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