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

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