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How much is Bill Gates worth? $61 BILLION Question: is that EXACTLY $61, 000,000,000.00????? Significant Figures 1 Significant Figures A measurement is always limited by the precision of the Instrument. An understanding of significant figures is important to express the appropriate precision of a measurement • Only zeros are non-significant digits (but not all always) • There are cases where a zero may be significant: 1. A Zero between 2 non-zeros digits. (103 cm) 2. Numbers less than 1, Zeros in front of the first non zero digit are not significant. (after start counting, they are significant) 0.002030 km (the last zero indicates measurement has been made that far out). 3. Numbers greater than 1, Zeros at the end of numbers do not refer to a precise count 980000 (There are exceptions: decimal points, bar over) 2 Significant Figures • 0.004070 -- The zeros shown in red are not significant. The number is precise to 4 significant digits • With numbers having a zero at the end the number of significant figures depends on the precision with which the number is known (how far was it measured). • 40000 -- one significant digit. The number is known to the nearest ten thousand. _ • 40000 -- three significant digits. The number is known to the nearest _ hundred. • 40000 -- five significant digits. The number is known to the nearest unit. 3 Significant Figures Practice: # of sig figs • 101 • 200 • 100.00 • 0.0008 • 0.005600 _ • 30 780 000 • 30 780_ 000 • 30 780 000 Answers: 3 1 5 1 4 8 4 5 4 Scientific Notation • Large numbers are hard to visualize. Scientific notation writes numbers in two parts: – a number between 1 and less than 10 and – a power of 10 • Examples • 30 000 000 is represented as 3 x 107 • 0.0000482 is represented as 4.82 x 10-5 • Note: The numbers present in Sci. Not. are SIGNIFICANT!!! 5 Scientific Notation Practice: • 0.0065 • 21 500 • 0.1408 • 589420 • 0.000 000 000 1 • 20 000 000 000 000 000 Answers: • 6.5 x 10-3 • 2.15 x 104 • 1.408 x 10-1 • 5.8942 x 105 • 1 x 10-10 • 2 x 1016 6 Significant Figures • Math Functions: Addition/subtraction: • When adding or subtracting, answer will have FEWEST decimal places. – Dumb People Are Stupid Multiplying/dividing: • When multiplying or dividing, answer with fewest Sig. Figs. – My Dad Sells Fireworks 7