PowerPint Significant Digits in Calculations, IsotopesPowerPoint在计算有效数字，同位素.pptVIP

How big? Significant Digits How small? How accurate? Reminder: bring a calculator to class Scientific notation Read “Scientific Notation” on page 621 Complete the chart below 9.07 x 10 – 2 0.0907 5.06 x 10 – 4 0.000506 2.3 x 1012 2 300 000 000 000 1.27 x 102 127 Scientific notation Decimal notation How can you tell which digits are significant All non zero numbers are significant All zeros that are located between two non zero numbers are significant Zeros that are located to the left of a value are not significant Zeros that are located to the right of a value may or may not be significant. How many significant digits in each? 2.83 36.77 14.0 0.0033 0.02 0.2410 2.350 x 10 – 2 1.00009 3 0.0056040 3 4 3 2 1 4 4 6 infinite 5 Significant Digits It is better to represent 100 as 1.00 x 102 Alternatively you can underline the position of the last significant digit. E.g. 100. This is especially useful when doing a long calculation or for recording experimental results Don’t round your answer until the last step in a calculation. Note that a line overtop of a number indicates that it repeats indefinitely. E.g. 9.6 = 9.6666… Similarly, 6.54 = 6.545454… Adding with Significant Digits The value with the fewest number of decimal places, going into the calculation determines the number of decimal that you should report in your answer. Adding with Significant Digits E.g. a) 13.64 + 0.075 + 67 b) 267.8 – 9.36 13.64 0.075 67 80.715 81 267.8 9.36 258.44 – + + Do the following 4.02 83.14 i) 83.25 0.1075 – 4.02 0.001 + ii) 1.82 0.2983 1.52 + iii) Multiplication and Division The value with the fewest number of significant digits, going into the calculation determines the number of significant digits that you should report in your answer. E.g. a) 608.3 x 3.45 b) 4.8 ? 392 a) 3.45 has 3 sig. digits, so the answer will as well 608.3 x 3.45 = 2098.635 = 2.10 x 103 b) 4.8 has 2 sig. digits, so the answer will