Significant Figures

Significant Figures Each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

Accuracy and Precision A number can only be as accurate and precise as the instrument that has made the measurement to produce that number. Accuracy refers to how close a measured value is to an accepted value. Precision refers to how close a series of measurements are to one another.

What is the difference? Let’s take a look at an archery contest to determine what accuracy and precision really are!

The arrow in the center of the target demonstrates high accuracy. Accuracy vs. Precision Accurate The arrow in the center of the target demonstrates high accuracy.

The arrows have all hit the same location but not the center. Accuracy vs. Precision Precise…NOT accurate The arrows have all hit the same location but not the center.

Accuracy vs. Precision Accurate and Precise The arrows are both precise (in the same place) and accurate (in the bull’s-eye).

Neither accurate or precise. Accuracy vs. Precision Neither accurate or precise. The arrows fail to hit the same location nor do they hit the intended location (center).

Rules for Significant Figures  1. All digits 1-9 are significant. Example: 213 has 3 significant digits)   2. Zeros between significant digits are always significant. Example: 3,013 has 4 significant digits. 3. Trailing zeroes in a number are significant only if the number contains decimal point. Example: 200.0 has 4 significant digits and 200 has 1 significant digit.

Rules for Significant Figures   4. Zeros in the beginning of a number whose only function is to place the decimal point are not significant. Example: 0.0043 has 2 significant digits. 5. Zeros following a decimal significant figure are significant. Example: 0.000342 has 3 significant digits and 0.43000 has 5 significant digits.

Calculations using Significant Figures Multiplication and Division When multiplying and dividing, limit and round the number to the least number of significant figures in any of the factors.   Example: 32.0 cm x 123 cm x 14 cm = 55,104 cm3 *The answer is written as: 55,000 because 14 has only TWO significant digits.

Calculations using Significant Figures Adding and Subtracting When adding and subtracting, limit and round the number to the least number of decimal places in any of the numbers that make up the answer.   Example: 122.53 mg + 39.0 mg x 82.327 mg = 243.857 mg *The answer is written as: 243.8 because 39.0 has only ONE significant digit.

How many significant figures are in each number? Practice Problems How many significant figures are in each number? a) 0.02 b) 0.040 c) 602 d) 3,000 e) 0.2010 Answers: a) 1, b) 2 , c) 3 d) 1 e) 4