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Chapter 2

Chapter 2. Significant Calculations And Scientific Notation. Section 3 Using Scientific Measurements. Chapter 2. Significant Figures, continued Rounding. Section 3 Using Scientific Measurements. Chapter 2. Addition or Subtraction with Significant Figures.

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Chapter 2

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  1. Chapter 2 Significant Calculations And Scientific Notation

  2. Section3 Using Scientific Measurements Chapter 2 Significant Figures, continued Rounding

  3. Section3 Using Scientific Measurements Chapter 2 Addition or Subtraction with Significant Figures • When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. • Example: • 2.001 + 3.0 = 5.0 • 0.0989 + 10.0 = 10.1

  4. Addition or Subtraction with Significant Figures • For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. • Example: • 2.00 x 1 = 2 • 2.01 x 4.003 = 8.05

  5. Section3 Using Scientific Measurements Chapter 2 Significant Figures, continued • Sample Problem E • Carry out the following calculations. Expresseach answer to the correct number of significantfigures. • a. 5.44 m - 2.6103 m • b. 2.4 g/mL  15.82 mL

  6. Section3 Using Scientific Measurements Chapter 2 Significant Figures, continued • Sample Problem E Solution • a. 5.44 m - 2.6103 m =2.83 m There should be two digits to the right of the decimal point, to match 5.44 m. b.2.4 g/mL  15.82 mL =38 g There should be two significant figures in the answer, to match 2.4 g/mL.

  7. Section3 Using Scientific Measurements Chapter 2

  8. Section3 Using Scientific Measurements Chapter 2 Scientific Notation, continued • In Scientific Notation, the coefficient is a number equal or larger than 1 but less than 10. • Example: • 3.5 may be a coefficient. • 0.9 may not • 90.3 may not

  9. Section3 Using Scientific Measurements Chapter 2 Scientific Notation, continued Mathematical Operations Using Scientific Notation 1. Addition and subtraction—These operations can be performed only if the values have the same exponent (n factor). example:4.2 × 104 kg + 7.9 × 103 kg or

  10. Section3 Using Scientific Measurements Chapter 2 Scientific Notation, continued Mathematical Operations Using Scientific Notation 2. Multiplication —The M factors are multiplied, and the exponents are added. example:(5.23 × 106 µm)(7.1 × 10−2 µm) = (5.23 × 7.1)(106 × 10−2) = 37.133 × 104 µm2 = 3.7 × 105 µm2

  11. Section3 Using Scientific Measurements Chapter 2 Scientific Notation, continued Mathematical Operations Using Scientific Notation 3. Division —The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. example: = 0.6716049383 × 103 = 6.7  102 g/mol

  12. Section3 Using Scientific Measurements Chapter 2 Direct Proportions • Two quantities are directly proportional to each other if dividing one by the other gives a constant value. • read as “y is proportional to x.”

  13. Section3 Using Scientific Measurements Chapter 2 Direct Proportion

  14. Section3 Using Scientific Measurements Chapter 2 Inverse Proportions • Two quantities are inversely proportional to each other if their product is constant. • read as “y is proportional to 1 divided by x.”

  15. Section3 Using Scientific Measurements Chapter 2 Inverse Proportion

  16. Worksheets

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