Scientific Notation and Significant Figures

Format is your choice. Suggestions: – Do NOT write down everything that is on the board. Include important definitions and practice problems. – Two column notes (Important Ideas on left, details and examples on right) – Listen and complete practice problems, then review at home tonight (the last step is important!) Chem Notes:

Just a Little Review…

How would you read the two graduated cylinders to the right? Turn and talk with your neighbor: What is the Limit of Precision?

Scientific Notation The Power of 10 Video Why Scientific Notation? Scientists sometimes have to deal in very large or very small quantities, and scientific notation is a way of expressing that number. Remember the Power of 10?

How To: Scientific Notation Rules to Follow: A positive exponent indicates that the number is greater than 1. Example: 1,500,000.0 = 1.5 x 10 6 A negative exponent indicates that the number is less than 1. Example: = 2.5 x Decimal Notation Scientific Notation: Coefficient must be between 1 and 9

Scientific Notation Practice! On your Scientific Notation WS: Convert the following to scientific notation: , , ,000,000

Scientific Notation Practice! On your Scientific Notation WS: Convert the following to decimal (standard) notation: x x x x x 10 5

Prefix 1 Exa = 1 Peta = 1 Tera = 1 Giga = 1 Mega = 1 kilo = 1 BASE UNIT 1 deci = 1 centi = 1 milli = 1 micro = 1 nano = 1 pico = 1 femto = 1 atto = Symbol E P T G M k  -- d c m µ n p f a # of Base Units (meters) =

Do all numbers matter? Not all numbers in a value are “significant.” Significant digits show the accuracy and precision of a measurement. Yesterday we said that this measurement was 5.1 mL. We estimated the 0.1 because the limit of precision is to the tenths place. That 5.1 is a significant digit.

NON-ZERO NUMBERS RULE 1. All non-zero numbers ARE significant. Value Sig Figs 8 mm 1 42 lbs?

Leading Zeros RULE 2. Leading zeros in decimal numbers are NOT significant. Value Sig Figs mm oz lb? mL ?

Sandwiched Zeros RULE 3. Zeros between nonzero numbers are significant. Value Sig Figs 50.8 mm min lb? m ?

Trailing Zeros RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. Value Sig Figs 25,000 in yr3 48,600 gal? 25,005,000 g ?

Significant Figures Practice! On your Significant Figures WS: Determine the number of significant figures in the following: , ,001

Calculations Using Sig Figs There are different rules for different mathematical operations: RULE: When adding and subtracting the answer is limited not by the significant digits, but the limit of precision! Example: mL mL mL = The calculated answer is mL The reported answer is rounded to the tenths place because 46.0 mL has the lowest limit of precision (least amount of decimal places). The answer is mL

Calculations Using Sig Figs There are different rules for different mathematical operations: RULE: When multiplying and dividing the answer has the same number of significant digits as the value with the fewest. Example: 23.0 cm x 432 cm x 19 cm = The calculated answer is 188,784 cm 3 The reported answer is rounded to two sig figs because 19 cm has the least amount in the problem. The answer is 190,000 cm 3