Scientific Notation & Significant Figures in Measurement

In science, we deal with some very LARGE numbers: 1 mole = We also deal with some very SMALL numbers: Mass of an electron = kg Scientific Notation

Imagine the difficulty of calculating the mass of 1 mole of electrons! kg x x ???????????????????????????????????

Scientific Notation: A method of representing very large or very small numbers in the form: M x 10 n M x 10 n  M is a number between 1 and 10  n is an integer For really large and really small numbers, a convenient way to represent them is by using:

Step #1: Insert an understood decimal point. Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n

2.5 x 10 9 The exponent is the number of places we moved the decimal. Note the exponent is positive because the original number was greater than 1.

Step #1: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #2: Count how many places you bounce the decimal point the decimal point Step #3: Re-write in the form M x 10 n 12345

5.79 x The exponent is negative because the original number was less than 1.

Characteristics of Measurement Part 1 - number Part 2 – unit of measure Examples: 20 grams 6.63 x Joule seconds Measurement - quantitative observation consisting of 2 parts consisting of 2 parts

The Fundamental SI Units (le Système International, SI)

SI Prefixes Common to Chemistry PrefixUnit Abbr.Exponent kilok10 3 decid10 -1 centic10 -2 millim10 -3 micro  10 -6

Uncertainty in Measurement A digit that must be estimated is called uncertain. –All measurements have 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 Accuracy Accuracy 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

More on Precision… Precision also refers to the smallest calibrated markings on laboratory instruments and equipment. –T–The precision of our triple beam balances is 1/10 th of a gram. –T–The precision of a 100 mL graduated cylinder is 1 milliliter. –T–The precision of our laboratory thermometers is one degree Celsius.

Significant Figures Significant figures in lab measurements and calculations are all of the certain and the one uncertain (estimated) digits recorded in measurements.

Rules for Counting Significant Figures Exact numbers (definitions and counting numbers) have an infinite number of significant figures.Exact numbers (definitions and counting numbers) have an infinite number of significant figures. 1 inch = 2.54 cm, exactly

Rules for Counting Significant Figures Nonzero integers always count as significant figures.Nonzero integers always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Zeros - Leading zeros do not count as significant figures has 3 sig figs.

Rules for Counting Significant Figures - Zeros - Captive zeros always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Zeros Trailing zeros are significant ONLY if the number contains a decimal point has 4 sig figs has 9300 has 2 sig figs.

Rules for Counting Significant Figures – Scientific notation The first term of a number written in scientific notation contains the significant figures x 10 9 has 4 sig figs. 4 x has 4 x has 1 sig fig.

Sig Fig Practice #1 How many significant figures in each of the following measurements? m  5 sig figs kg  4 sig figs 100,890 L  5 sig figs 3.29 x 10 3 s  3 sig figs cm  2 sig figs 3,200,000  2 sig figs

Rules for Rounding If the digit immediately following the one to be rounded is 5 or greater, round UP. If not, do not change the digit. 81,053 rounded to 3 sig figs is 81, rounded to 2 sig figs is 6.3.

Sig Figs & Rounding Practice Round to 3 sig figs. Round to 1 sig fig. Round to 2 sig figs. Round x to 3 sig figs Round 45 to 1 sig fig. Round 67 to 5 sig figs x x

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement =  18.7 (1 place after the decimal)

Rules for Significant Figures in Mathematical Operations Multiplication and Division: The number of sig figs in the result equals the number in the least precise measurement used in the calculation x 2.0 =  13 (2 sig figs)

Sig Fig Practice # m m CalculationCalculator says: Correct Answer m g g g 0.02 cm cm cm L L L lb lb lb mL mL mL

Sig Fig Practice # m x 7.0 m CalculationCalculator says: Correct Answer m g ÷ 23.7 cm g/cm cm x cm cm m ÷ 3.0 s m/s lb x 3.23 ft lb·ft g ÷ 2.87 mL g/mL