Scientific Notation Often used to express very large or very small numbers. Also used to maintain correct number of significant figures.

Form:(# from 1 to 9.999) x 10 exponent 800= 8 x 10 x 10 = 8 x = x 10 x 10 x 10 = x = 1.4 / 10 / 10 / 10 = 1.4 x 10 –3

Change to standard form x 10 –5 = x 10 8 = 370,000, x 10 1 = x 10 –2 =

Change to scientific notation. 12,340 = x = 3.69 x 10 – = 8 x 10 –3 1,000,000,000 = 1 x 10 9

Using the Exponent Key on a Calculator EXPEE

EE or EXP means “times 10 to the…” How to type out 6.02 x : 6EE y x x EE320y x 32 x Don’t do it like this… …or like this… …or like this: How to type out 6.02 x : 6EE WRONG! TOO MUCH WORK.

Also, know when to hit your (–) sign… …before the number, …after the number, …or either one.

Example: 1.2 x x But instead is written… = 1. 2EE Type this calculation in like this: This is NOT written…4.3 – –09 Calculator gives… E–09 or… 4.3 x 10 –9 4.3 E –9or

Scientific Notation Converting Numbers to Scientific Notation How to Use a Scientific Calculator

Scientific Notation We often use very small and very large numbers in chemistry. Scientific notation is a method to express these numbers in a manageable fashion. Thus cm can be written 1 x cm. Lets see why… Scientific notation expresses a number as the product of two factors, the first falling between 1 and 10 and the second being a power of 10.

Scientific Notation 5000 = 5 x 10 3 or x (10 x 10 x 10) 5 x Numbers > one have a positive exponent. Numbers < one have a negative exponent. EE Numbers are written in the form M x 10 n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number. x 10 n

Converting Numbers to Scientific Notation x In scientific notation, a number is separated into two parts. The first part is a number between 1 and 10. The second part is a power of ten.

How to Use a Scientific Calculator How to enter this on a calculator: EE EXP = rounded to 6.7 x 10 2 ENTER Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52. Divide: (5.44 x 10 7 ) (8.1 x 10 4 ).. OR

Rule for Multiplication Calculating with Numbers Written in Scientific Notation When multiplying numbers in scientific notation, multiply the first factors and add the exponents. Sample Problem: Multiply 3.2 x by 2.1 x 10 5 (3.2) x (2.1) = 6.72 (-7) + (5) = -2 or x Exercise: Multiply 14.6 x 10 7 by 1.5 x x 10 12

Rule for Division Calculating with Numbers Written in Scientific Notation When dividing numbers in scientific notation, divide the first factor in the numerator by the first factor in the denominator. Then subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide 6.4 x 10 6 by 1.7 x 10 2 (6.4) (1.7) = 3.76 (6) - (2) = 4 or x 10 4 Exercise: Divide 2.4 x by 3.1 x x

Rule for Addition and Subtraction Calculating with Numbers Written in Scientific Notation In order to add or subtract numbers written in scientific notation, you must express them with the same power of 10. Sample Problem: Add 5.8 x 10 3 and 2.16 x 10 4 (5.8 x 10 3 ) + (21.6 x 10 3 ) =27.4 x 10 3 Exercise: Add 8.32 x and 1.2 x x x 10 4

Using Scientific Notation for Expressing the Correct Number of Significant Figures Measurement Number of significant figures it contains Measurement Number of significant figures it contains 25 g kg x 10 6 mg 6 x 10 4 sec g cm m 0.12 kg cm kg 6.00 x 10 6 kg 409 cm cm g

27dFields-Jeff/intro1.htm Scientific Notation