Significant Digits (Figures) As they relate to Accuracy and Precision

Accuracy vs. Precision What is Precision? Precision is NOT how right or wrong a measurement or answer to a problem is. Precision tells one how consistent a measuring device is.

Or how closely do your measurements match up to each other when you have data from multiple trials. Example: Most Precise Trial Brad Suzi Mac 1 46.5 mL 45.6 mL 47.8 mL 2 46.4 mL 45.5 mL 47.9 mL 3 42.3 mL 40.7 mL Ranges from 42.3 to 46.5 – that’s a 4.2 spread. Ranges from 47.8 to 47.9 – that’s a 0.1 spread. Ranges from 40.7 to 45.6 – that’s a 4.9 spread.

Precision may be affected by: mechanical errors human error (malfunctions of equipment) human error (you goofed!) environmental errors (i.e. changes in temperature or air pressure – things beyond your control.)

What is Accuracy? How close a measured (observed) value is to the accepted (expected) value How do we determine the accuracy of our measurements? In science, accuracy is defined in terms of how wrong our answer is!

Relative Percent Error So we report our accuracy in % error. How do we determine the relative % error? By using the following formula: lValue actual – Value experimental l x 100% Value actual Practice: You determined that the mean of your experiment was 25.6 seconds. The accepted value is 24.8 seconds. What is your % error?

Solution l24.8 s – 25.6 sl x 100 % 24.8 s = 3.23%

Significant Digits The number of digits in a number will let you know how precise and hopefully how accurate your measurement was. The more digits that are after the decimal point in your measurement, the more precise your measurement was.

HOWEVER!!! You cannot arbitrarily decide on the number of digits to put your answer in. The measuring tool will determine this. So-o-o, how do you know how many significant digits are in a number? Just follow this simple method!

A P Decimal Is present Is absent If a then then 0.0050074 60038954000 8 sig figs 5 sig figs

Drill and Practice Underline the significant digits in each of the following numbers and indicate the number of the rule or rules that apply. 0.00506970 500.6790 250005 4970350000 5678493 6 sig figs 7 sig figs 6 sig figs 6 sig figs 7 sig figs

How to Decide How Many Significant Digits in an Answer When adding or subtracting, use “after decimal” rule. Look at the numbers that you are adding or subtracting and identify the number that has the least number of digits after the decimal. Your answer can only have that number of digits after the decimal.

Example 2.2 + 40.05 + 0.00325 = 42.25325 Function = addition so use the after decimal rule. 2.2 has 1 digit after the decimal, 40.05 has 2, and 0.00325 has 5. The answer can only have 1 digit after the decimal. So my Answer = 42.3

When doing math problems, the number of significant digits depends upon the math function you are doing. When multiplying or dividing, use the “least number” rule. Look at all the numbers you are given in the problem and find the one that has the least number of significant digits in it. Your answer can only have that number of significant digits in it.

Example 2.25 x 0.55 x 7.00 = 8.6625 Function = multiplication so use least number rule. 2.25 has 3 s.d., 0.55 has 2 s.d., 7.00 has 3 s.d., so my answer can only have 2 s.d’s in it. So my answer is 8.7

4.52 x 6.6 = 29.832 = 30. 0.5550 x 2.46 = 3.015 = 3.02 755.55 x 0.000355 = 0.26822 = 0.268 68492 / 49000 = 1.397795918 = 1.4 0.000345 / 0.003500 = 0.0985714 = 0.0986