Accuracy How close you measure or hit a true value or target
Precision How many times you measure the same quantity or how many times you hit the exact same position
Significant Figures Measured digits with no known certainty. + or – an amount Uncertain last digit Rules to know how many significant figures are in a number (sig. figs.) 35.3 could be 35.3 (+ or -.1), so could have measured it at 35.2 or 35.4. Depends on how you round it up or down.
0 Rule All non zero numbers are significant Place holders are not significant Measured zero is significant
Rule 1 Zeros between nonzero numbers are significant 507.2 = 4 sig. figs. 1.0048 = 5 sig. figs. These numbers were all actually measured.
Rule 2 Zeros to the right of a decimal and in front of the number are not significant.0048 = 2 sig. figs. First two numbers were not actually measured, they are place holders. 1.0048 = 5 sig. figs. All of these numbers were measured.
Rule 3 Zeros to the right of a decimal and end of the number are significant 3.620 = 4 sig. figs. Because all the numbers had to have been measured. Could have been 3.619 or 3.621, so 0 at the end is the uncertainty number, no other reason to have put it there unless it was measured and rounded.
Rule 4 Zeros at the end of a whole number may or may not be significant. 170 pounds. No one knows if the last number was measured or estimated. 1.70 x 10 2 means all the numbers are significant and the last one is uncertain. 1.7 x 10 2 means that all the numbers are accurate and were measured.
Adding sig. figs How many numbers to the right of a decimal that you have in your answer, depends on the measured number with the least amount of sig. figs. 5.36 + 2.4 = 7.76 = 7.8 = 2 sig. figs. Same with subtraction
Rounding off Rules when adding or subtracting First non-significant number at the end of the number is extra, you don’t need it. Rule 1 –above 5 = +1 Rule 2 –under 5 = use the same number Rule 3 –if it is 5 and the next number is 1-9, +1 -if it is 5 and the next number is 0 or not there, look at the number before the 5. If it is even then use the same number, if it is odd, then +1. 7.225 = 7.22 7.275 = 7.28
Multiplication Rules No more numbers in your answer than is in the least sig. fig. number that you measured. 203.5 x 4.0 means your answer should have only 2 sig. figs. 203.5 x 4.0 = 814.00 Round the 4 down = 810 and the 0 is a place holder so 8.1 x 10 2 = 2 sig. figs.