Problem Solving in Chemistry 2.2 & 2.3

What are Significant Digits?

Significant Digits are all of the digits that you know plus one final digit that is estimated or uncertain. Example: mL of liquid

Significant Digits Can easily be determined using the Atlantic-Pacific rules

Significant Digits Atlantic-Pacific rules: Decimal Present – count from the Pacific

Significant Digits Atlantic-Pacific rules: Decimal Present – count from the Pacific Find the first non-zero digit Everything to the right is significant

Significant Digits Atlantic-Pacific rules: Decimal Absent– count from the Atlantic

Significant Digits Atlantic-Pacific rules: Decimal Absent– count from the Atlantic Find the first non-zero digit Everything to the left is significant

Significant Digits Examples: 115 volts amperes grams 0.20 miles meters g 4.0  g 3201 g 4100 mi mi 4100 mi 4.1  10 3 mi 200,001 cm m

Significant Digits Examples: 207 ft g 610. liters cm milliliters 72,000 L m 627,005 g

Significant Digits Special Cases: Counted quantities have an unlimited number of significant digits Examples: 10 cars 5,500 apples 1 dozen pencils

Significant Digits Special Cases: Exact Conversions have an unlimited number of significant digits Examples: 1 km = 1000 m 1 m = 100 cm 1 ft = 12 in

How are Significant Digits used in problems?

Significant Digits in Math Problems Multiplication/Division: General Rule: The product or quotient contains the same number of significant figures as the measurement with the least amount of sig. digs.

Significant Digits in Math Problems Multiplication/Division Rules: count the sig digs in each number determine which number has the smallest amount of sig digs do the calculation round off the answer so it has the same amount of sig digs as the number with the least amount of sig digs

Significant Digits in Math Problems Multiplication/Division Examples: 1.25 g × 8.6  C = g  25.0 mL = cm × cm = g  85.2 cm 3 =

Significant Digits in Math Problems Addition/Subtraction: General Rule: The sum or difference contains the same number of decimal places as the measurement with the least number of decimal places.

Significant Digits in Math Problems Addition/Subtraction Rules: line up the decimal points do the calculation round off the answer so that the final digit is in the same place as the leftmost uncertain digit

Significant Digits in Math Problems Addition/Subtraction Examples: 38 cm cm cm = g – g = km – 0.54 km = m m =

Significant Digits Review: What is the number of significant digits in each of the following? 54.0 kg g 1,100 m 12 eggs

Significant Digits Review: Round the following number to the specified number of sig. digs. 468,

Significant Digits Review: Perform the following operations. Express the answers with the correct number of sig. digs kg kg 5.44 m – m 6.9 g/mL × mL g / mL

What is Dimensional Analysis?

Dimensional Analysis is a method that uses cross- cancellation and equality statements to convert from one unit to another.

How is Dimensional Analysis used?

Dimensional Analysis Examples: In a 5-lb bag of apples, there are about 20 Michigan apples. How many apples would there be in a 1-lb bag?

Dimensional Analysis Examples: Assume that there are 80 apples in a bushel and a tree could produce 32 bushels of apples. How many five-pound bags of apples did the tree produce?

Dimensional Analysis Examples: There are 21 peanut M&Ms in a 1.74 oz bag. How many would be in a 2.00 lb bag?

Dimensional Analysis Examples: A production line at the peanut M&M factory is able to produce lb bags every minutes. How many M&Ms are produced in an hour?

Dimensional Analysis Examples: You are driving in Canada. Your speed reads 55 mi/hr. Their speed limit is 70 km/hr. Are you speeding?

Dimensional Analysis Examples: A person claims to be able to run at a speed of 3.5 meters per second. Convert this to miles per hour. Do you think the person is lying? (Show your work.)