Precision, Accuracy & Significant Figures

Today in class, we learned about precision, accuracy, but mostly significant figures.
Here are some definitions...


Precision - how reproducible measurement is compared to other similar measurements.
Accuracy - how close the (average) measurement  comes to the accepted or real value.
Significant Figures - measured in meaningful digits and the more precise means the more significant digits.


A - Significant Digits
- the last digit in a measure is uncertain as it could be one digit higher or lower. 
[ example: 3.24L. The 3 & 2 are certain whereas the 4 is uncertain ]
- significant digits in the measurement include ALL of the certain and first uncertain digit.
[ example: 3.24 = 3 sig figs ]


B - Significant Figures: Digits
- leading zero are not counted.
[ example: 0.04 = 1 sig fig ]
- trailing zeros after the decimal point are counted.
[ example: 10.0230 = 6 sig figs ]
- trailing zeros without a decimal point are not counted.
[ example: 15100 = 3 sig figs ]


C - Exact Numbers
- some quantities are defined as exactly a certain amount and no rounding is required.
- have an infinite number of sig figs.
[example: 4 dogs can be expressed as 4.000 dogs]
[example: a "pair" of shoes = 2 shoes (not 1.853892 shoes rounded up to 2) ]


D - Rounding Rules
1. look at the digit after the position of rounding.
2. if the digit is <5, round down.
3. if the digit is >5, round up.
4. if the digit is =5, and there are more non-zero digits after the 5, round up.
5. if that digit is =5 and it ends at the 5, round to make the last digit an even number.


Here are some practice rounding questions: round to the nearest tenth.
a) 26.73 =
b) 26.79 =
c) 15.31 =
d) 83.298634 =
e) 62.4585 =


Answers:
a) 26.7
b) 26.8
c) 15.3
d) 83.3
e) 62.5


E - Math Rules: Adding & Subtracting
- when adding and subtracting, round to the fewest number of decimal places (least precise).
[example: 12.544g + 1.3g = 13.844 ---> 13.8 (1.3 only has one decimal place) ]
here's a visual example:













F - Math Rules: Multiplying & Dividing
- when multiplying and dividing, round to the fewest sig figs.
[example: 12.27g x 3.8g = 46.626 ---> 47g(squared) ]
[example: 24.845g(squared) / 1.3g = 19.11 ---> 19g ]
visual example:

















hope this helped!
submitted by Kimberly Leung:)