Unit One Notes: Significant Figures

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Presentation transcript:

Unit One Notes: Significant Figures 2.3

A. What are Significant Figures? The number of all certain digits in a measurement plus one estimated digit.

Example 1 2 3 4 cm 2 Significant figures 2.0 cm

Examples 1 2 3 4 cm 3 Significant figures 3.0 cm 5

B. Rules for counting Significant Figures Any number that is not a zero is significant Sandwiched Zeros are always significant Leading Zeros (zeros before a nonzero) are never significant Trailing Zeros (zeros after a nonzero) are sometimes significant (only if a decimal is present) Counting numbers and defined constants have an infinite number of significant figures.

B. Rules for Significant Figures Rule 1. All non-zeros are significant Ex: 3456 has ____ significant figures 4 1 2 3 4 5 6 7 8 9

B. Rules for Significant Figures Rule 2. Sandwiched zeros are always significant Ex: 1,007 has ____ significant figures 4 Zeros

B. Rules for Significant Figures Rule 3. Leading zeros are never significant Ex: 0.0486 has ____ significant figures 3 Zeros

B. Rules for Significant Figures Rule 4. Trailing zeros are sometimes significant. Trailing and with a decimal point and the the right of a nonzero are significant Ex: 9.300 has ____ significant figures Ex: 31,000 has ____ significant figures 4 2 Zeros

Rules for Significant Figures Rule 5: unlimited sig figs happen in 2 situations Counting = 32 people in class = Infinite sig figs Exact defined quantities (1 hr = 60 min)= Infinite sig figs

Examples: An engineer made the following measurements. How many significant figures are in each measurement? 1.0070 m 20 g/mL 17.10 kg 20 meter sticks 100,890 L 1.090 s 0.0054 cm 0.00200 g 5 1 unlimited 4 4 5 2 3

C. Rules for Rounding Significant Figures If the number is less than 5, the last digit is unchanged. If the number is 5 or more, the last significant digit is increased by 1 Trick: A bar may be written over the last significant figure

Examples: Round the following to 3 significant figures 2.541 2.859 24,585 1.0001 1,589 5899 0.005697 22,999 2.54 2.86 1.00 24,600 1,590 5900 23,000 0.00570

Practice Determine the number of sig. figs for each value given. a) 0.54 = __________ sig figs b) 0.0098 = __________ sig figs c) 2370 = __________ sig figs d) 16070 = __________ sig figs e) 160.0 = __________ sig figs f) 37000 = __________ sig figs 2 2 3 4 4 2

Practice Round each of the following to 3 sig figs a) 458900 b) 258000.0 c) 784643 d) 45.097 e) 0.00086432 f) 0.06598 459000 258000 785000 45.1 0.000864 0.0660