8/29/11

• 1. Room Map

• 2. Tally Skills Test

• 3. E-2 Significant figures notes

• 4. E-2 Practice Problems

Significant FiguresAs you learned in the measurement activity, an appropriate measurement for the length of the rectangle below is 3.65 cm. Because the “3” and the “6” are certain, and the “5” is our guess, all three digits are intentional or “significant.” Thus 3.65 cm contains three significant figures.

0 1 2 3 4 5cm

Significant FiguresThe scale below is less precise, and so the rectangle’s length should be reported as just 3.5 cm. This measurement has just two significant figures: the “3” and the “5” and it is considered to be a weaker, less valuable measurement than 3.65 cm.

0 1 2 3 4 5cm

Significant FiguresThe scale below, however, is more precise, and a magnified view (shown at right) is helpful in making a good reading: 3.665 cm. This measurement has 4 significant figures: the “3.66…” which are certain, and the “5” which is the guess.

0 1 2 3 4 5cm

(3.6) (3.7)

Significant Figures3.5 cm has two significant figures,

3.65 cm has three significant figures, 3.665 cm has four significant figures. You might start to think that the number of significant figures is simply equal to the number of digits there are in a measurement, but that is not always the case…

Significant FiguresConsider the length of the rectangle below: 3500 mm. The “3” is definite. The “5” is the guess. So what about the two zeroes at the end? Are they significant?

0 1000mm

2000 3000 4000 5000

Significant FiguresConsider the length of the rectangle below: 3500 mm. The “3” is definite. The “5” is the guess. So what about the two zeroes at the end? Are they significant?

NO! They are not considered significant.

0 1000mm

2000 3000 4000 5000

Significant FiguresIn 3500 mm, the zeroes are serving a very different purpose than the “3” and the “5.” These two zeroes are acting as place-keepers. They show the size of the measurement -- 3500 mm, not just 35 mm – but they do not make the measurement any more precise.

0 1000mm

2000 3000 4000 5000

Significant FiguresThus 3500 mm has just two significant figures, not four.

0 1000mm

2000 3000 4000 5000

Significant FiguresNow consider the measurement below: 3450 mm. How many significant figures does it have? (Make a guess before continuing.)

0 1000mm

2000 3000 4000 5000

Significant FiguresNow consider the measurement below: 3450 mm. How many significant figures does it have? (Make a guess before continuing.)

If you said three, you are correct!

0 1000mm

2000 3000 4000 5000

Significant FiguresIn 3450 mm, the “3” and “4” are definite and the “5” is the guess, so those are the three significant figures. The zero at the end is a place-keeping zero, and so it is not considered to be significant.

0 1000mm

2000 3000 4000 5000

Significant FiguresNow what about the measurement below: 0.00275 m? How many significant figures do you think it has? (Make a guess before continuing.)

0 0.001m

0.002 0.003 0.004 0.005

Significant FiguresNow what about the measurement below: 0.00275 m? How many significant figures do you think it has? (Make a guess before continuing.)

If you said three, good job.

0 0.001m

0.002 0.003 0.004 0.005

Significant FiguresIn 0.00275 m, the “2” and “7” are definite and the “5” is the guess. Here the zeroes in the beginning of the number are place keepers. They make 0.00275 a small number, just as the zeroes in 3500 make it a big number.

0 0.001m

0.002 0.003 0.004 0.005

Significant FiguresIf you are good at converting numbers into scientific notation then this will help:

170,000,000,000 converts into 1.7 x 1011.

And 0.00000563 converts into 5.63 x 10-6.

170,000,000,000 converts into 1.7 x 1011.

And 0.00000563 converts into 5.63 x 10-6. Notice how scientific notation separates out all the significant figures and puts them in the beginning…

1.7 x 1011 5.63 x 10-6

170,000,000,000 converts into 1.7 x 1011.

And 0.00000563 converts into 5.63 x 10-6. Notice how scientific notation separates out all the significant figures and puts them in the beginning…and it changes all the place-

keeping zeroes into a power of ten

1.7 x 1011 5.63 x 10-6

Significant Figures3500 has two significant figures,

0.00275 has three significant figures.

You might start to think that zeroes are never significant, but that is not always the case…

Significant FiguresConsider the measurement shown below:

30.5 cm.

0 10cm

20 30 40 50

30.5 cm. Here the zero is one of the significant figures: the “3” and the “0” are definite, and the “5” is the guess.

0 10cm

20 30 40 50

30.5 cm. Here the zero is one of the significant figures: the “3” and the “0” are definite, and the “6” is the guess.

30.5 cm has three significant figures.

0 10cm

20 30 40 50

Significant FiguresAnd consider the measurement shown below:

23.0 cm.

0 10cm

20 30 40 50

23.0 cm. Here the zero is also one of the significant figures: the “2” and the “3” are definite, and this time the “0” is the guess.

0 10cm

20 30 40 50

23.0 cm. Here the zero is also one of the significant figures: the “2” and the “3” are definite, and this time the “0” is the guess.

23.0 cm has three significant figures.

0 10cm

20 30 40 50

Rules recap thusfar:

Rules for identifying significant figures in a measurement:1. All non-zero digits are significant (i.e. 1-9).2. 2. All zeros or groups of zeros between non zero digits are significant (ex. ALL the zeros in 703 g, 8.001 mL, and 7010.02 cm are all significant because of rule #2a.)

AND all zeros between a non-zero digit on the left and a decimal on the right are also significant (ex. ALL the zeros in

140. cm, 6000. mL, are 1800. g are all significant because of rule #2b.). These 2 types of zeros can be referred to as “squeezed zeros.”3. All zeros or groups of zeros to the right of the decimal AND at the end of the number are significant (ex. ALL the zeros in

2.30 cm, 7.00 mL, and 56.9000 g are all significant because of rule #3.). These zeros can be referred to as “trailing zeros.”**ALL other types of zeros are NOT significant and serve only as place holders (ex. The zeros in 300 cm and 0.0071 mL ARE NOT significant

since they are neither “squeezed zeros” nor “trailing zeros”). Remember, significant means measured, not important (Place holder zeros ARE still important even if they aren’t significant!)!

All those rules seem a bit tough to keep straight?

While you should remember why we do sig figs, and what makes something “significant,”

here’s a handy trick to help you count your sig figs:

If the decimal point is Absent, count from the Atlantic.

If the decimal point is Present, count from the Pacific.

________________________________________________________________

For example: 6702000 has no decimal point. The Altantic rule applies!

|<---- starting from the “Atlantic,” heading “west,”

the first non-zero digit we hit is the 2, and everything after that is also significant. So 6702000 has 4 significant figures!

SHORTCUT! HANDY TRICK!

If the decimal point is Absent, count from the Atlantic.

If the decimal point is Present, count from the Pacific.

We’ll stop here for Day 1 of E2

Day 1 Homework:

Bottom of page 10 in WB

#1 ALL,

#2 a-h

Want more practice? Keep going on these slides from the blog (MHSchemistry.wordpress.com)!

There’s a good recap at slide #130, just before Day 2 notes pick up.

Significant FiguresNow, let’s see how much you have learned about significant figures.

What follows are 50 different problems. For each one, simply think of the how many significant figures there are, then go to the next slide to see if you are correct. If you are correct, go on to the next problem. If not, try to figure out why your answer is incorrect.

Significant Figures

34.84 cm

Significant Figures

34.84 cm4 sig figs

Significant Figures

63 g2 sig figs

Significant Figures

109 m3 sig figs

Significant Figures

17.03 cm

Significant Figures

17.03 cm4 sig figs

Significant Figures

290 mm

Significant Figures

290 mm2 sig figs

Significant Figures

0.00037 s

Significant Figures

0.00037 s2 sig figs

Significant Figures

0.00405 kg

Significant Figures

0.00405 kg3 sig figs

Significant Figures

70400 mL

Significant Figures

70400 mL3 sig figs

Significant Figures

0.03040 L

Significant Figures

0.03040 L4 sig figs

Significant Figures

33.0 J

Significant Figures

33.0 J3 sig figs

Significant Figures

2500.0 cm

Significant Figures

2500.0 cm5 sig figs

Significant Figures

600 mg

Significant Figures

600 mg1 sig fig

Significant Figures

0.0041050 m2

Significant Figures

0.0041050 m2

5 sig figs

Significant Figures

0.00023 s

Significant Figures

0.00023 s2 sig figs

Significant Figures

55 mi/hr

Significant Figures

55 mi/hr2 sig figs

Significant Figures

5.62 x 107 mm

Significant Figures

5.62 x 107 mm3 sig figs

Significant Figures

8 x 10-4 g

Significant Figures

8 x 10-4 g1 sig fig

Significant Figures

3.0 x 1014 atoms

Significant Figures

3.0 x 1014 atoms2 sig figs

Significant Figures

0.03050 L

Significant Figures

0.03050 L4 sig figs

Significant Figures

4050 g

Significant Figures

4050 g3 sig figs

Significant Figures

0.0360 g/mL

Significant Figures

0.0360 g/mL3 sig figs

Significant Figures

41,000 mm

Significant Figures

41,000 mm2 sig figs

Significant Figures

25.0 oC

Significant Figures

25.0 oC3 sig figs

Significant Figures

3.00 x 104 ms

Significant Figures

3.00 x 104 ms3 sig figs

Significant Figures

5 x 10-7 K

Significant Figures

5 x 10-7 K1 sig fig

Significant Figures

0.0000401 L

Significant Figures

0.0000401 L3 sig figs

Significant Figures

30200 cm3

Significant Figures

30200 cm3

3 sig figs

Significant Figures

210.4 cg

Significant Figures

210.4 cg4 sig figs

Significant Figures

340 km

Significant Figures

340 km2 sig figs

Significant Figures

340.0 km

Significant Figures

340.0 km4 sig figs

Significant Figures

0.500 Hz

Significant Figures

0.500 Hz3 sig figs

Significant Figures

0.0050400 m

Significant Figures

0.0050400 m5 sig figs

Significant Figures

50,400 m

Significant Figures

50,400 m3 sig figs

Significant Figures

23,000 cm

Significant Figures

23,000 cm2 sig figs

Significant Figures

23.000 cm

Significant Figures

23.000 cm5 sig figs

Significant Figures

1,000,000 mi

Significant Figures

1,000,000 mi1 sig fig

Significant Figures

1,000,001 mi

Significant Figures

1,000,001 mi7 sig figs

Significant Figures

0.30 mL

Significant Figures

0.30 mL2 sig figs

Significant Figures

4.00 x 103 g

Significant Figures

4.00 x 103 g3 sig figs

Significant Figures

0.0998 s

Significant Figures

0.0998 s3 sig figs

Significant Figures

530 m2 sig figs

Significant Figures

7 km1 sig fig

Significant Figures

400 kg

Significant Figures

400 kg1 sig fig

Significant Figures

0.0032 m3

Significant Figures

0.0032 m3

2 sig figs

Significant Figures

7060 g/L

Significant Figures

7060 g/L3 sig figs

Significant FiguresSo… How did you do? With more practice, you should be able to zip through those problems with no mistakes!

Significant FiguresAlthough you have not been given any specific rules about whether or not a digit in a number is significant or not, see if you can figure out those rules for yourself:

(write your list of rules in your notebook.)

For example, what about nonzero digits (like 2 or 7): when are they significant?

For example, what about nonzero digits (like 2 or 7): when are they significant? And what about zeroes: when are they significant?

Significant FiguresWhen you have finished your list, make sure it covers all cases: zeroes in the beginning of numbers, in the middle and at the end… with decimal points and without…. with lines and without…scientific notation…

Then compare your set of rules to the ones that follow:

Significant FiguresHere is one way to represent the rules for significant figures:

Nonzero digits (26.3) are always significant.(so 26.3 has three significant figures)

Zeroes occur in three different places in a number:

If they are at the beginning (0.005), they are never significant.(so 0.005 has one significant figures)

If they are in the middle (1207), they are always significant.(so 1207 has four significant figures)

And if they are at the end, they are sometimes significant.

If there is a decimal point (21.600) they are significant.(so 21.600 has five significant figures)

If there is no decimal point (21600), they are not significant.(so 21600 has three significant figures)

Significant FiguresThe only exception to those rules is when there is a line over a zero (630000). When there is a line over a zero, treat that zero like a nonzero digit. So 630000 would have four significant figures. But Mrs. A won’t use this in Chem 1.

As for scientific notation (3.40 x 106), it follows these same rules if you just ignore the “times ten to the whatever power.” Or, simply put, every digit to the left of the times sign is automatically significant.

So 3.40 x 106 has three significant figures.

DAY 2 of E2 (sig figs)Remember that “significant” means “measured”.

We should always report our measurements as accurately as possible with the tools we are using. (Measure to the smallest mark the scale allows, then estimate one more decimal beyond).

We went over the rules yesterday, and I also shared a handy trick with you (the “Atlantic-Pacific Rule”):

If the decimal is If the decimal is Present, count Absent, countfrom the Pacific from the Atlantic.

Let’s go over the Practice Problems! Pg 10 in WB:

1. How many significant figures are in each of the following?

a. 2.020 cm e. 0.022 cm i. 2200 cm

b. 202 mL f. 2.2 mL j. 0.0220 mL

c. 0.202 g g. 20.0 g k. 2.0200 g

d. 200 kg h. 200. kg l. 2.0 x 103 kg

p. 10 #2 a-h

2. How many sig figs in the following?

a. 365 m

b. 42,000 L

c. 1030 mm

d. 0.414 cm

e. 0.00842 m

f. 42.0 L

g. 6.4 x 103 mm

h. 3.00 x 10-1 cm

What happens when we do math with our measurements?

So you’ve accurately measured in the lab and reported with the correct sig figs… now what?

For example, let’s say you measured 2.35 gpressing on an area of 6.70 cm2.

Calculate the pressure in grams per cm2; 2.35g ÷ 6.70 cm2

What does your calculator say?

Probably 0.35074627! Did you measure to the millionths? No! We need some more sig fig rules to save us from these runaway, misleading digits!

Sig Figs in Addition + Subtraction:

When adding or subtracting measurements, determine which measurement has the fewest significant PLACES (= your least precise measurement).

1062 m 632.8687 kg + 410 m - 427.20 kg 1472 m = 1470 m 205.6687 kg = 205.67 kg

After calculating, ROUND your answer to only as many significant PLACES as that least precise measurement that was used in the calculation.

Sig Figs in Multiplication & Division:

When multiplying or dividing measurements, determine which measurement has the fewest TOTAL significant figures (= your least precise measurement).

3 m x 102 m = 306 m2 = 300 m2

0.072 g ÷ 0.10788 mL = 0.6674082… g/mL = 0.67 g/mL

Don’t forget to round the last digit as needed(if the first dropped digit is 5 or greater, round UP).

When calculating with labels, don’t forget to add, subtract, multiply, or divide the labels, too! (cm x cm = cm2) (g ÷ mL = g/mL)

HOMEWORK:

1. Look over Safety Notes (quiz tomorrow!)2. Get Safety Contract signed3. Don’t forget the Career Wksht is due Friday.

4. P.P. page 11 from WB due tomorrow.

Do these on a separate paper, not in WB!!!

#3: a & b

8/29/11

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