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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?)

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**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)

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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)

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Practice Hebden p.37 #55

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

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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

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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)!

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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?

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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?

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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

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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

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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

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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

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**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

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**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)

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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

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**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

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**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

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**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

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Homework Sig figs worksheet #1 and 5

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**Calculations Using Sig Figs**

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**Multiplication & Division**

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

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**Multiplication & Division**

2.391 x 4.5 = ?

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**Multiplication & Division**

2.391 x 4.5 = ? 4 sig figs x 2 sig figs = ?

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**Multiplication & Division**

2.391 x 4.5 = ? 4 sig figs x 2 sig figs = ? 4 sig figs x 2 sig figs = 2 sig figs

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**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 =

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**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)

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**Multiplication & Division**

Practice: Hebden p.39 #56

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**Addition & Subtraction**

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

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**Addition & Subtraction**

= ?

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**Addition & Subtraction**

= ? 3 decimals + 2 decimals = ?

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**Addition & Subtraction**

= ? 3 decimals + 2 decimals = 2 decimals

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**Addition & Subtraction**

= ? 3 decimals + 2 decimals = 2 decimals = round to 2 decimals

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**Addition & Subtraction**

= ? 3 decimals + 2 decimals = 2 decimals = round to 2 decimals = 2 decimals, 4 sig figs

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**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

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**Addition & Subtraction**

2.45 x x 104 = ? 2.45 x x 105 = ?

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**Addition & Subtraction**

2.45 x x 104 = ? 2.45 x x 105 = ? 2.45 x x 105 = 2.76 x 105

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**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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