Transcript 1-4 Notes
Chapter 1 Introduction to Physical Science Section 4: Mathematics and Science What math skills do scientists use in collecting data and making measurements? Estimation: • An approximation of a number based on known/ reasonable information • Scientists cannot always obtain EXACT numbers • Example: measuring distances between stars Accuracy and Reproducibility Accuracy: • How close a measurement is to the true value • Example: If you were playing darts, accurate throws land close to the bull’s-eye Reproducibility: • How close a group of measurements are to each other • Example: Reproducible throws land close to one another Scientists aim for both accuracy and reproducibility in their measurements. Chapter 1 Introduction to Physical Science Significant Figures • A measurement should contain only those numbers that are significant. Rules to Sig Figs: Significant figures in a measurement include all of the digits that are known precisely plus one last digit that is estimated. Here is a handout that discusses these rules….. Let’s look at it now! Non-zero digits are always significant. 103.230002 All final zeros after the decimal point are significant. 12.740 ; 0.0420 Zeros between two other significant digits are always significant. 10.0 ; 2004 ; 6.000 Zeros used only for spacing the decimal point are not significant. 100 ; .00000233 Adding or Subtracting • If you add or subtract, the answer is rounded to the same number of decimal places as the measurement with the least number of decimal places. • Example: 5.3 cm (1 decimal place) + 21.94 cm (2 decimal places) 27.24 cm ≈ 27.2 cm (1 decimal place) Chapter 1 Introduction to Physical Science Multiplying and Dividing Measurements • When you multiply or divide measurements, your answers can have only the same number of significant figures as the measurement with the fewest significant figures. 2.25 m X 3m 6.75 m2 ≈ 7 m2 You Try!!! How many sig figs do each of these numbers have? 1) 2) 3) 4) 5) .004560 750 606,950 7,050.00 8.00003 Answers: 1) 4 2) 2 3) 5 4) 6 5) 6 Scientific Notation • Scientific notation is the way that scientists easily handle very large numbers or very small numbers. • For example, instead of writing 0.0000000056, we write 5.6 x 10-9 • How does this work? • Let’s take a look at your handout on Scientific Notation and do some examples on the board!