Significant FiguresHonors Chemistry I

Uncertainty in Measurement

A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Why Is there Uncertainty?Measurements are performed with

instruments. No instrument can read to an infinite number

of decimal places Which of these balances has the greatest uncertainty in measurement?

Precision and AccuracyAccuracy refers to the agreement of a

particular value with the true value. Precision refers to the degree of agreement

among several measurements made in the same manner.

Neither accurate nor precise

Precise but not accurate

Precise and accurate

Types of errorRandom Error (indeterminate Error) –

measurement has an equal probability of being high or low.

Systematic Error ( Determinate Error) – Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.

Percent error

% error = |experimental value – theoretical value| x 100%

theoretical value

Rules for Counting Significant Figures

Nonzero integers- Every nonzero digit in a reported measurement is assumed to be significant.3456 has 4 significant figures

Rules for Counting Significant FiguresZeros Leading zeros do not count as significant figures. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such place holding zeros.0.0486 has3 significant figures0.000099 has 2 significant figures

Rules for Counting Significant FiguresZerosSandwiched zeros : ( zeros appearing between nonzero digits) always count as significant figures.

16.07 has4 significant figures7003 has 4 significant figures

Rules for Counting Significant FiguresZerosTrailing zeros are significant only if the number contains a decimal point.300 meters has 1 significant figure7000 has1 significant figure27,210 has Four significant figures

Zeros at the end of a number and to the right of a decimal point are always significant. 43.00 has Four significant figures1.010 has 4 significant figures9.000 has 4 significant figures

Exact numbers have an infinite number of significant figures. There are two situations in which numbers have an unlimited number of significant figures. 1. Counting, a number that is counted is exact. Ex. 28 people in your classroom- 2 significant figures.2. The second situation involves exactly defined quantities such as those found within a system of measurement. Ex. 60 min = 1 hr – unlimited number of significant figures100 cm = 1 m – unlimited number of significant figures

Sig fig Practice # 1How many significant figures in each of the following? 1.0070 m ---- 5 sig figs17.10 kg ----- 4 sig figs100,890 L -- 5 sig figs3.29 x 10^3 s -- 3 sig figs0.0054 cm -- 2 sig figs3,200,000 - 2 sig figs

Rules for significant figures in mathematical operationsMultiplication and Division – number of significant figures you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures. The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements. Ex. 6.38 x 2.0 = 12.76 - 13 (2 significant figures)

Rules for significant figures in mathematical operationsAddition and Subtraction: The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. 6.8 + 11.934=18.734 18.7 ( 3 sig figs)