Accuracy and Precision

In this class, for those of the people in physics, we reviewed accuracy and precision followed by significant digits.

Precision - how reproducible a measurement is compared to other similar measurements

EG: bounces of a basketball on one spot

Accuracy - how close the measure(or average measurement) comes to the accepted or real value.

EG: 2 + 2 = 4 (not 4.1 or 4.2 etc)

SIGNIFICANT FIGURES


-measured or meaningful digits
-more precise = more significant digits
-The last digit is considered uncertain(it could be one digit higher or lower).
-Includes all certain digits and the first uncertain****

Note: Leading 0's are not counted

EG: 0.00000000005 <--- only one significant digit
-Trailing 0's are counted

EG: 10.9029000
-If there is a decimal, count the zero as a significant digit.


EG: 100000.

EXACT NUMBERS


-Some quantities are defined exactly a certain amount and no rounding is required
-Exact numbers have an infinite amount of sig figs.


ROUNDING RULES


1) Look at the digit after the position of rounding
2) If >5 round up
3) If <5 keep it the same
4) If = 5 and more non-zero digits, round up
5) If = 5 and ends at five, round to make it even.

MATH RULES FOR SIG FIGS


-When adding or subtracting, round to the fewest number of decimals.
-When multiplying or dividing, round to the fewest number of sig figs.

MULTIPLYING AND DIVIDING

- When multiplying and or dividing, round to the fewest number of sig figs

E.g. 12.54 x 1.3 = 16.302 <-- you must round that to 16.30.

12.540/1.3 = 9.64 <-- you must round to 2 sig figs (2<4) or the first uncertain digit.