Significant Figures

1. Zeroes placed before other digits are not significant: example: 0 1. Zeroes placed before other digits are not significant: example: 0.0000023 only has 2 Significant figures. 2. Zeroes placed between other digits are always significant: example: 5008 has 4 significant figures. 3. Zeroes placed after other digits but behind a decimal point are significant: example: 2.90 has 3 significant figures. 4. Zeroes at the end of a number are significant only if they are behind a decimal point as in 3. Otherwise, it is impossible to tell if they are significant. 

Example: If you have 43000 you are not 100% sure if there are 2, 3,4 or 5 significant figures SO WHAT SHOULD YOU DO? Put them into scientific notation!  ex. 4.300 x 10⁴  has 4 significant figures       4.30 x 10⁴ has 3 significant figures       4.3 x 10⁴ has 2 significant figures

RULES OF MULTIPLICATION AND DIVISION: In a calculation involving multiplication and division the number of significant figures in an answer should equal the least number of significant figures in any one of the numbers being multiplied or divided. 

Example 1. 3.0m (2 sig figs) x 4.67m (3 sig figs) = 14 (2 significant figures) 2. 3000.0 km (5 sig figs) / 6.0 km (2 sig fig)     = 500 X *The answer cannot be 500 because it must only have 2 sig figs.        so we put it into scientific notation      = 5.0 x 10 to the 2nd

RULES OF ADDITION AND SUBTRACTION: In a calculation involving addition and subtraction, the number of decimal places (not significant figures) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.

Example 1. 3.98 (2 decimal places) + 4.3 (1 decimal place) + 4.66565632 (8 decimal places) = 12.9 ( 1 decimal place) 2. 39.00 (2 decimal place) - 5.543 (3 decimal places) + 3.33 (2 decimal places) = 36.79 (1 decimal place) * Even though it may seem tempting to make this answer 36.8, you CANNOT because you must have 2 decimal places according to the data that you received. 

Sins of significant figures 1. Writing more digits in an answer (intermediate or final) than justified by the number of digits in the data.  2. Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.