Significant Digits and Scientific Notation

Accuracy vs Precision An accurate measurement is close to the true value. Precision gives an idea of the reliability of a measurement Precision is a measure of the agreement among a series of measurements.

Significant Digits Significant digits are the digits in a measurement that are known to be precise

Which digits are significant? Not Significant Non-zero digits Zeros in the middle Zeros at the end As long as there is a decimal point somewhere in the number Exact numbers and integers have infinite significant figures Leading zeros “ x10n ” in scientific notation

1000 1000. 01000 1 x 103 1.0 x 103 87032 74000 8.900 0.000342 0.002190

Don't round off or drop zeros. Your calculator is not included. Sig. Figs. in Lab All of the digits in the readout a digital apparatus are significant and should be written down. Don't round off or drop zeros. Your calculator is not included.

Analog Scales The digit not read from the written scale is the estimated digit Example: 82.5mL estimated digit = 5 Analog scales are read to one tenth of the smallest graduation present. Example: Scale is graduated every 1 mL, so reading should be to the nearest 0.1 mL. Don't round off or drop zeros. Example: 29.0mL

Calculations with Sig. Figs. Calculations involving measurements Significant figures depends on the sig figs of the measurements The weakest link principle Least number of sig figs is limiting One rule for addition and subtraction different rule for multiplication and division.

Addition and Subtraction RULE: When adding and subtracting, the result should have the same number of decimal places as the least precise number added. Example: 26.098 + 3.92 = 534.1-265.36 =

Multiplication and Division RULE: When multiplying or dividing, the result should have the same number of significant figures as the number with least significant figures. Example: 3.28 x 2.1 87.008 ÷ 7.20

Longer Calculations In a calculation with several steps, the final result must be rounded off to the correct sig. figs. Rounding off intermediate results may cause cumulative round-off errors. Don’t round until the end. (2.34 x 1.3) + 23.18 = 8.35 – 2.73 +(5.31 ÷ 3.001)=

Scientific Notation Use scientific notation to eliminate place holding zeros. Move the decimal so that only 1 digit remains in front of the decimal. Then change the exponent accordingly. If you move the decimal to the right the exponent is negative. If you move the decimal to the left the exponent is positive Round to the correct number of sig figs 43200000 0.00264

When taking a number out of scientific notation move the decimal in the opposite direction and fill the empty spaces with 0’s If the exponent is negative move the decimal point to the left If the exponent is positive move the decimal point to the right 3.46 x 10-5 8.138 x 108