Significant Figures Significant figures are important in science

Significant Figures Significant figures are important in science as they convey uncertainty in measurements and calculations involving measurement. In science, there are no repeating decimal values. Every value has a specific number of digits which are used to express it due to uncertainty in measurement and measuring instruments.

Significant Figures • Significant figures are a simple means for conveying uncertainty associated with a measurement. • They are frequently employed when only one or two measurements are made instead of a series of measurements from which an average (mean) and uncertainty could be determined. • A significant figure or significant digit is one known with reasonable reliability.

Significant Figures cont’d • Rules for determining significant digits in a measured value. • All digits in a measurement are considered significant except for place holding zeros whose function is to provide the value with its magnitude. Therefore, magnitude of a number has nothing to do with its significance. 1. All nonzero digits (1 – 9) are significant. 2. All zeros between significant digits are significant. 3. Zeros ending a number to the right of the decimal are significant. 4. Zeros ending a number to the left of the decimal point are not significant unless so indicated. – Indications may be expression of the decimal point or a repitand bar over the last significant zero. 5. Zeros to the left of significant digits are not significant.

Significant Figures cont’d • It is important to recognize that numbers moving into or out of scientific notation form do not alter their significance! • e. g. 2, 300 in -----> 2. 3 x 10+3 in • 10. 0 g ------> 1. 00 x 10+1 • 2. 35 x 10 -5 Mm ------>0. 000 023 5 Mm • 4. 00 x 10+4 μL ------> 40, Ō00 μL

MAKE A NOTE!! • NOTE: All problems given on tests and quizzes in this class will be expressed to the desired significance. Treat them accordingly!!!

Operations Using Significant Figures • Addition and subtraction • When adding or subtracting, identify the least significant value on a units/decimal place basis. – Value with largest uncertainty • Perform the operation (addition or subtraction). • Round the result to the same units/decimal place as the least significant value.

Operations Using Significant Figures • Multiplication and division • When multiplying or dividing, identify the least significant value based upon the number of significant digits. • Perform the operation (multiplying or dividing). • Round the result to have the same number of significant digits as the least significant figure.

Rules for Rounding • 1. If the first digit dropped is less than 5, leave the preceding number unchanged. (3. 123 becomes 3. 12) • 2. If the first digit dropped is greater than 5, increase the preceding digit by 1. (3. 127 becomes 3. 13) • 3. If the first digit dropped is exactly 5, round off to make the preceding digit an even number. (4. 125 becomes 4. 12, but 4. 135 becomes 4. 14) – Exactly 5, (or 1/2), means there could be any number of zeros after the five, however, no nonzero digits.