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Understanding Measurements: Significant Figures, Scientific Notation, and Dimensional Analysis

Learn about significant figures, scientific notation, and dimensional analysis in the real world of measurements. Discover the rules for identifying significant figures, converting numbers to scientific notation, and performing dimensional analysis. Practice examples provided.

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Understanding Measurements: Significant Figures, Scientific Notation, and Dimensional Analysis

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  1. Significant figures Scientific Notation Dimensional analysis Measurements

  2. Significant Figures • In the real world, no measurement is exact. The relative exactness of a measurement is its accuracy • In a measured value, all the digits that are known to be exact are called significant digits. Zeros at the end of a whole number are assumed to be non-significant.

  3. Rules for identifying Significant Figures

  4. Independent Practice • 9004507 m has ___ significant figures • 0.00000860092 s has __ sig. figs. • 102.00 kg has ___ sig. figs. • The ruler reads 700 g, so your measurement has ___ sig. figs. • 1.02 x 105 s has ___sig. figs.

  5. Scientific Notation • Used for very large or very small numbers.  • Made up of three parts: the coefficient, the base and the exponent.  567 000 in sci. notation is: 5.67 x 105         coefficient           base        exponent

  6. Standard to Sci. Notation • Move decimal as many times to make a number between 1 and 10 • Coefficient is always followed by x 10 • Exponent = number of times you move the decimal • Large # = ( + )exponent • Small # = ( - )exponent • Example: What is 238,000 in Sci. Notation?

  7. Independent Practice • 597800000 • 0.00004507 • 2500000000 • 0.0023

  8. Sci. Notation to Standard • Move the decimal as many times as the exponent is worth • Positive exponent = move to the  • Negative exponent = move to the  • Fill spaces with zeros • Example: What is 1.56 x 105 in Standard notation?

  9. Independent Practice • 2.36 x 108 • 7.8 x 10-3 • 3.92 x 10-5 • 5.43 x 105

  10. Dimensional Analysis • It is a method used to convert from one unit to another • Consists of 3 Steps to get your answer • 1.) Identify the Given and the Unknown • 2.) Identify the Conversion factor needed to go from one unit to another • 3.) Set up the problem • 4.) Multiply across at the top and divide by the bottom

  11. Example • How many kg are in 3.42 grams?

  12. Independent Practice • 500 ft = ______________________ m • 5750 mL= _________________ L • 0.024 km= __________________m • 432 minutes = ________________ hrs

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