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Significant Figures A significant figure (sig fig) is a measured or meaningful digit Sig figs are made of all the certain digits of a measurement plus the first uncertain digit (the extra digit you had to guess remember?)

Significant Figures Non-zeroes are significant
Zeroes between sig figs are significant - e.g. 101 (3), (5) 3. Zeroes at the end of numbers without decimals are not significant - e.g. 10 (1), 100 (1), 1100 (2), (3)

Significant Figures 4. Zeroes at the end of numbers with decimals are significant - e.g (4), 1.00 (3), (5) Zeroes in front of numbers with decimals are not significant - e.g (1), (2), (3)

Practice Hebden p.37 #55

Problem with Rule #3 How can we express 10,000 as 5 sig figs if the zeroes at the end are not significant?

Problem with Rule #3 How can we express 10,000 as 5 sig figs if the zeroes at the end are not significant? The bad way: add a decimal at the end 10,000. Do not do this in Chem 11…or ever But you still need to recognize they mean 5 sig figs when that’s written

Problem with Rule #3 How can we express 10,000 as 5 sig figs if the zeroes at the end are not significant? The good way: use scientific notation (exponents)!

Problem with Rule #3 How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant? Use scientific notation (exponents)! 10,000 = ? x 10?

Problem with Rule #3 How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant? Use scientific notation (exponents)! 10,000 = x 10?

Problem with Rule #3 How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant? Use scientific notation (exponents)! 10,000 = x 104

Problem with Rule #3 How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant? Use scientific notation (exponents)! 10,000 = x 104 Rule #4: Zeroes at the end of numbers with decimals are significant

Scientific Notation When you move a decimal right, you must multiply by 0.1 = x 0.1 x 0.1 x 0.1 x 0.1 = x 10-1 x 10-1 x 10-1 x 10-1 = x 10-4 When you move a decimal left, you must multiply by 10 12345 = x 101 x 101 x 101 x 101 = x 104

Standard Notation These are the “regular” numbers without the exponents (the opposite if you will) You need to know how to convert b/t the 2 Positive exponent: move decimal right 3.385x102  338.5 Negative exponent: move decimal left 3.385x10-2 

Practice Conversions Express the following in scientific notation
10.124 Express the following in standard notation 7.002 x 10-3 1.63 x 102 x 10-2

Rounding Some of us are used to always rounding 5s up
E.g  21 In Chem 11, we will round 5s to the nearest even number E.g  20 (20 is nearer than 22) E.g  22 (22 is nearer than 20)

Arrow Rule for Sig Figs If there is decimal: arrow starts from the left   sig figs If no decimal: arrow starts from the right  00 7 sig figs Arrow moves until it hits a non-zero Count the numbers that are left when the arrows stops and those are your sig figs 4 or 5 volunteers to help demonstrate please

Arrow Rule for Sig Figs Form 4 lines
Inside lines face out, outside lines face in Each line is a team One team makes up a number while the other team uses the arrow rule to determine the number of sig figs in that number Switch roles after 1 person answers Everyone must answer at least once

Arrow Rule for Sig Figs Use the cards I’ve given to make numbers
Move around to change the order Can hold 0, 1 or 2 cards in your hands Hold them up and show the other team when you’re done so they can answer Tally up scores and the winners can go against each other

Arrow Rule for Sig Figs +1 point for every correct answer
-1 point for every “bad” number made up E.g 184. Try to let the arrow figure it out themselves Remember: it’s not about the outcome, it’s about the process

Homework Sig figs worksheet #1 and 5

Calculations Using Sig Figs

Multiplication & Division
Round the answer to the least number of sig figs contained in the question 2.391 x 4.5 = ?

Multiplication & Division
2.391 x 4.5 = ?

Multiplication & Division
2.391 x 4.5 = ? 4 sig figs x 2 sig figs = ?

Multiplication & Division
2.391 x 4.5 = ? 4 sig figs x 2 sig figs = ? 4 sig figs x 2 sig figs = 2 sig figs

Multiplication & Division
2.391 x 4.5 = ? 4 sig figs x 2 sig figs = ? 4 sig figs x 2 sig figs = 2 sig figs 2.391 x 4.5 =

Multiplication & Division
2.391 x 4.5 = ? 4 sig figs x 2 sig figs = ? 4 sig figs x 2 sig figs = 2 sig figs 2.391 x 4.5 =  11 (2 sig figs)

Multiplication & Division
Practice: Hebden p.39 #56

Addition & Subtraction
Round off the answer to the least precise number in the problem Remember that least precise means fewest decimal places

Addition & Subtraction
= ?

Addition & Subtraction
= ? 3 decimals + 2 decimals = ?

Addition & Subtraction
= ? 3 decimals + 2 decimals = 2 decimals

Addition & Subtraction
= ? 3 decimals + 2 decimals = 2 decimals =  round to 2 decimals

Addition & Subtraction
= ? 3 decimals + 2 decimals = 2 decimals =  round to 2 decimals =  2 decimals, 4 sig figs

Addition & Subtraction
2.45 x x 104 = ? Must convert to the same exponent to see which is less precise Always convert the smaller exponent into the larger one

Addition & Subtraction
2.45 x x 104 = ? 2.45 x x 105 = ?

Addition & Subtraction
2.45 x x 104 = ? 2.45 x x 105 = ? 2.45 x x 105 = 2.76 x 105

Practice Hebden p.28-34 #42-50, p.37 #55 (was HW)
Add/subtract: Hebden p.40 #57 All operations: Hebden p. 40 #58-59 Hand in sig figs worksheet (online).

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