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Significant Figure Rules 1 4 Rules to determine how many significant figures are in a number: 1. Non-zero digits are always significant. 2. Zeros between two numbers are significant. 3. Zeros to the left of the number are never significant 4. Zeros to the right of a number are only significant if there is a decimal point. 2 Something to think about… Because all measurements are uncertain, we must only use those numbers that are meaningful. A common ruler cannot measure something to be 22.4072643 cm long. Not all of the digits have meaning (significance), and therefore should not be written down. In science, only the numbers that have significance (derived from measurement) are written. 3 Rule 1: Non-zero digits are always significant. If you measure something and the device you use (ruler, thermometer, triple-beam balance, etc.) returns a number to you, then you have made a measurement decision and that ACT of measuring gives significance to that particular numeral (or digit) in the overall value you obtain. Ex: 26.38 = 4 sig. figures Ex: 7.94 = 3 sig. figures. THE PROBLEM: numbers such as 0.00980 or 28.09. 4 Rule 2: Any zeros between two numbers are significant. Ex: 406 By the first rule, the 4 and 6 are significant. However, to make a measurement decision on the 4 (in the hundred’s place) and the 6 (in the unit’s place), you HAD to have made a decision on the ten’s place. 5 Rule 3: Zeros to the left of the number are never significant Space holding zeros on numbers less than one. 0.00500 0.03040 These zeros serve only as space holders. They are there to put the decimal point in its correct location. They do NOT involve measurement decisions. When you write them in scientific notation (5.00 x 10-3 and 3.040 x 10-2), the non-significant zeros disappear! 6 Rule 4: Zeros to the right of a number are only significant if there is a decimal point. This rule causes the most difficulty. Here are two examples of this rule with the zeros this rule affects in red: 0.00500 0.03040 Here are two more examples where the significant zeros are in red: 2.30 x 10-5 4.500 x 1012 7 Rule 4: Zeros to the right of a number are only significant if there is a decimal point. 200 is considered to have only ONE significant figure while 25,000 has two. This is based on the way each number is written. When whole numbers are written as above, the zeros, BY DEFINITION, did not require a measurement decision, and so they are not significant. If you want 200 to have 2 sig. figures, write it in scientific notation: 2.0 x 102 For 3 sig. figures, write 2.00 x 102 or with a decimal at the end: 200. 8 Infinite Significance Numbers that are not measured are considered to have infinite significance Counting numbers 36 cars 50 people 200,000,000 grains of sand Definitions 1 m = 1000 mm The boiling point of water is 100°C 9 Some Practice: How many significant digits are there in each of the following quantities? Why? Answers A. B. C. D. E. F. G. H. I. J. A. B. C. D. E. F. G. H. I. J. 20 kg 0.0051 g 11 m 0.010 s 90.4 degrees Celsius 0.004 cm 0.089 kg 0.009 00 L 100.0 degrees Celsius 20 cars 1 2 2 2 3 1 2 3 4 infinite 10