To start the tutorial push the f5 key in the upper row on your keyboard
This presentation is the property of its rightful owner.
Sponsored Links
1 / 154

To start the tutorial, push the f5 key in the upper row on your keyboard PowerPoint PPT Presentation


  • 80 Views
  • Uploaded on
  • Presentation posted in: General

f5. To start the tutorial, push the f5 key in the upper row on your keyboard. Then you can use the up and down arrow keys to advance backwards and forwards through the tutorial. Significant Figures.

Download Presentation

To start the tutorial, push the f5 key in the upper row on your keyboard

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


To start the tutorial push the f5 key in the upper row on your keyboard

f5

To start the tutorial, push the f5 key in the upper row on your keyboard

Then you can use the up and down arrow keys to advance backwards and forwards through the tutorial.


Significant figures

Significant Figures

As you learned in a previous tutorial, an appropriate measurement for the length of the rectangle below is 3.76 cm. Because the “3” and the “7” are certain, and the “6” is our guess, all three digits are intentional or “significant.” Thus 3.76 cm contains three significant figures.

0

1

2

3

4

5

cm


Significant figures1

Significant Figures

The scale below is less precise, and so the rectangle’s length should be reported as just 3.8 cm. This measurement has just two significant figures: the “3” and the “8” and it is considered to be a weaker, less valuable measurement than 3.76 cm.

0

1

2

3

4

5

cm


Significant figures2

Significant Figures

The scale below, however, is more precise, and a magnified view (shown at right) is helpful in making a good reading: 3.764 cm. This measurement has 4 significant figures: the “3.76…” which are certain, and the “4” which is the guess.

(3.7)

(3.8)

0

1

2

3

4

5

cm


Significant figures3

Significant Figures

3.7 cm has two significant figures,

3.76 cm has three significant figures,

3.764 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 figures4

Significant Figures

Consider the length of the rectangle below: 3200 mm. The “3” is definite. The “2” is the guess. So what about the two zeroes at the end? Are they significant?

5000

4000

3000

2000

0

1000

mm


Significant figures5

Significant Figures

Consider the length of the rectangle below: 3200 mm. The “3” is definite. The “2” is the guess. So what about the two zeroes at the end? Are they significant?

NO! They are not considered significant.

5000

4000

3000

2000

0

1000

mm


Significant figures6

Significant Figures

In 3200 mm, the zeroes are serving a very different purpose than the “3” and the “2.” These two zeroes are acting as place-keepers. They show the size of the measurement -- 3200 mm, not just 32 mm – but they do not make the measurement any more precise.

5000

4000

3000

2000

0

1000

mm


Significant figures7

Significant Figures

Thus 3200 mm has just two significant figures, not four.

5000

4000

3000

2000

0

1000

mm


Significant figures8

Significant Figures

Now consider the measurement below: 3190 mm. How many significant figures does it have? (Make a guess before continuing.)

5000

4000

3000

2000

0

1000

mm


Significant figures9

Significant Figures

Now consider the measurement below: 3190 mm. How many significant figures does it have? (Make a guess before continuing.)

If you said three, you are correct!

5000

4000

3000

2000

0

1000

mm


Significant figures10

Significant Figures

In 3190 mm, the “3” and “1” are definite and the “9” 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.

5000

4000

3000

2000

0

1000

mm


Significant figures11

Significant Figures

Now what about the measurement below: 0.00273 m? How many significant figures do you think it has? (Make a guess before continuing.)

0.005

0.004

0.003

0.002

0

0.001

m


Significant figures12

Significant Figures

Now what about the measurement below: 0.00273 m? How many significant figures do you think it has? (Make a guess before continuing.)

If you said three, good job.

0.005

0.004

0.003

0.002

0

0.001

m


Significant figures13

Significant Figures

In 0.00273 m, the “2” and “7” are definite and the “3” is the guess. Here the zeroes in the beginning of the number are place keepers. They make 0.00273 a small number, just as the zeroes in 3200 make it a big number.

0.005

0.004

0.003

0.002

0

0.001

m


Significant figures14

Significant Figures

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


Significant figures15

Significant Figures

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

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


Significant figures16

Significant Figures

If 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.


Significant figures17

Significant Figures

If 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. 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


Significant figures18

Significant Figures

If 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. 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 figures19

Significant Figures

3200 has two significant figures,

0.00273 has three significant figures.

6000000 has just one significant figure.

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


Significant figures20

Significant Figures

Consider the measurement shown below:

30.6 cm.

50

40

30

20

0

10

cm


Significant figures21

Significant Figures

Consider the measurement shown below:

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

50

40

30

20

0

10

cm


Significant figures22

Significant Figures

Consider the measurement shown below:

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

30.6 cm has three significant figures.

50

40

30

20

0

10

cm


Significant figures23

Significant Figures

And consider the measurement shown below:

23.0 cm.

50

40

30

20

0

10

cm


Significant figures24

Significant Figures

And consider the measurement shown below:

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.

50

40

30

20

0

10

cm


Significant figures25

Significant Figures

And consider the measurement shown below:

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.

50

40

30

20

0

10

cm


Significant figures26

Significant Figures

Sometimes a tricky situation occurs in which a zero looks like its in a place-keeping position, but we intend to have it be a guess.


Significant figures27

Significant Figures

Sometimes a tricky situation occurs in which a zero looks like its in a place-keeping position, but we intend to have it be a guess. Consider the measurement below: 2600 cm.

5000

4000

3000

2000

0

1000

cm


Significant figures28

Significant Figures

But if we write it simply as 2600 cm, it appears to have only two significant figures: the “2” being definite and the “6” being the guess.

5000

4000

3000

2000

0

1000

cm


Significant figures29

Significant Figures

But if we write it simply as 2600 cm, it appears to have only two significant figures: the “2” being definite and the “6” being the guess. But the guess is supposed to be first “0” following the “6.”

5000

4000

3000

2000

0

1000

cm


Significant figures30

Significant Figures

But if we write it simply as 2600 cm, it appears to have only two significant figures: the “2” being definite and the “6” being the guess. But the guess is supposed to be first “0” following the “6.” How do we make that zero look significant and not appear to be a place keeping zero?

5000

4000

3000

2000

0

1000

cm


Significant figures31

Significant Figures

By placing a line over it: 2600 cm.

5000

4000

3000

2000

0

1000

cm


Significant figures32

Significant Figures

By placing a line over it: 2600 cm.

(Sometimes placing a line over a number means that number gets repeated over and over forever: 0.3 = 0.3333333333…

5000

4000

3000

2000

0

1000

cm


Significant figures33

Significant Figures

By placing a line over it: 2600 cm.

(Sometimes placing a line over a number means that number gets repeated over and over forever: 0.3 = 0.3333333333… but in 2600, the line is being used to show that a zero in a place keeping position is actually significant.)

5000

4000

3000

2000

0

1000

cm


Significant figures34

Significant Figures

Now, 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 figures35

Significant Figures

34.84 cm


Significant figures36

Significant Figures

34.84 cm

4 sig figs


Significant figures37

Significant Figures

63 g


Significant figures38

Significant Figures

63 g

2 sig figs


Significant figures39

Significant Figures

109 m


Significant figures40

Significant Figures

109 m

3 sig figs


Significant figures41

Significant Figures

17.03 cm


Significant figures42

Significant Figures

17.03 cm

4 sig figs


Significant figures43

Significant Figures

290 mm


Significant figures44

Significant Figures

290 mm

2 sig figs


Significant figures45

Significant Figures

0.00037 s


Significant figures46

Significant Figures

0.00037 s

2 sig figs


Significant figures47

Significant Figures

0.00405 kg


Significant figures48

Significant Figures

0.00405 kg

3 sig figs


Significant figures49

Significant Figures

70400 mL


Significant figures50

Significant Figures

70400 mL

3 sig figs


Significant figures51

Significant Figures

0.03040 L


Significant figures52

Significant Figures

0.03040 L

4 sig figs


Significant figures53

Significant Figures

33.0 J


Significant figures54

Significant Figures

33.0 J

3 sig figs


Significant figures55

Significant Figures

2500.0 cm


Significant figures56

Significant Figures

2500.0 cm

5 sig figs


Significant figures57

Significant Figures

600 mg


Significant figures58

Significant Figures

600 mg

1 sig fig


Significant figures59

Significant Figures

0.0041050 m2


Significant figures60

Significant Figures

0.0041050 m2

5 sig figs


Significant figures61

Significant Figures

0.00023 s


Significant figures62

Significant Figures

0.00023 s

2 sig figs


Significant figures63

Significant Figures

55 mi/hr


Significant figures64

Significant Figures

55 mi/hr

2 sig figs


Significant figures65

Significant Figures

1400 g


Significant figures66

Significant Figures

1400 g

3 sig figs


Significant figures67

Significant Figures

1400 g


Significant figures68

Significant Figures

1400 g

4 sig figs


Significant figures69

Significant Figures

5.62 x 107 mm


Significant figures70

Significant Figures

5.62 x 107 mm

3 sig figs


Significant figures71

Significant Figures

8 x 10-4 g


Significant figures72

Significant Figures

8 x 10-4 g

1 sig fig


Significant figures73

Significant Figures

3.0 x 1014 atoms


Significant figures74

Significant Figures

3.0 x 1014 atoms

2 sig figs


Significant figures75

Significant Figures

0.03050 L


Significant figures76

Significant Figures

0.03050 L

4 sig figs


Significant figures77

Significant Figures

4050 g


Significant figures78

Significant Figures

4050 g

3 sig figs


Significant figures79

Significant Figures

0.0360 g/mL


Significant figures80

Significant Figures

0.0360 g/mL

3 sig figs


Significant figures81

Significant Figures

41,000 mm


Significant figures82

Significant Figures

41,000 mm

2 sig figs


Significant figures83

Significant Figures

41,000 mm


Significant figures84

Significant Figures

41,000 mm

4 sig figs


Significant figures85

Significant Figures

25.0 oC


Significant figures86

Significant Figures

25.0 oC

3 sig figs


Significant figures87

Significant Figures

3.00 x 104 ms


Significant figures88

Significant Figures

3.00 x 104 ms

3 sig figs


Significant figures89

Significant Figures

5 x 10-7 K


Significant figures90

Significant Figures

5 x 10-7 K

1 sig fig


Significant figures91

Significant Figures

0.0000401 L


Significant figures92

Significant Figures

0.0000401 L

3 sig figs


Significant figures93

Significant Figures

30200 cm3


Significant figures94

Significant Figures

30200 cm3

3 sig figs


Significant figures95

Significant Figures

30200 cm3


Significant figures96

Significant Figures

30200 cm3

4 sig figs


Significant figures97

Significant Figures

210.4 cg


Significant figures98

Significant Figures

210.4 cg

4 sig figs


Significant figures99

Significant Figures

340 km


Significant figures100

Significant Figures

340 km

2 sig figs


Significant figures101

Significant Figures

340.0 km


Significant figures102

Significant Figures

340.0 km

4 sig figs


Significant figures103

Significant Figures

0.500 Hz


Significant figures104

Significant Figures

0.500 Hz

3 sig figs


Significant figures105

Significant Figures

0.0050400 m


Significant figures106

Significant Figures

0.0050400 m

5 sig figs


Significant figures107

Significant Figures

50,400 m


Significant figures108

Significant Figures

50,400 m

3 sig figs


Significant figures109

Significant Figures

23,000 cm


Significant figures110

Significant Figures

23,000 cm

2 sig figs


Significant figures111

Significant Figures

23.000 cm


Significant figures112

Significant Figures

23.000 cm

5 sig figs


Significant figures113

Significant Figures

1,000,000 mi


Significant figures114

Significant Figures

1,000,000 mi

1 sig fig


Significant figures115

Significant Figures

1,000,001 mi


Significant figures116

Significant Figures

1,000,001 mi

7 sig figs


Significant figures117

Significant Figures

0.30 mL


Significant figures118

Significant Figures

0.30 mL

2 sig figs


Significant figures119

Significant Figures

4.00 x 103 g


Significant figures120

Significant Figures

4.00 x 103 g

3 sig figs


Significant figures121

Significant Figures

0.0998 s


Significant figures122

Significant Figures

0.0998 s

3 sig figs


Significant figures123

Significant Figures

14,300 s


Significant figures124

Significant Figures

14,300 s

4 sig figs


Significant figures125

Significant Figures

530 m


Significant figures126

Significant Figures

530 m

2 sig figs


Significant figures127

Significant Figures

7 km


Significant figures128

Significant Figures

7 km

1 sig fig


Significant figures129

Significant Figures

400 kg


Significant figures130

Significant Figures

400 kg

1 sig fig


Significant figures131

Significant Figures

0.0032 m3


Significant figures132

Significant Figures

0.0032 m3

2 sig figs


Significant figures133

Significant Figures

7060 g/L


Significant figures134

Significant Figures

7060 g/L

3 sig figs


Significant figures135

Significant Figures

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


Significant figures136

Significant Figures

Although 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.)


Significant figures137

Significant Figures

Although 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?


Significant figures138

Significant Figures

Although 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? And what about zeroes: when are they significant?


Significant figures139

Significant Figures

When 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…


Significant figures140

Significant Figures

When 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 figures141

Significant Figures

Here is one way to represent the rules for significant figures:


Significant figures142

Significant Figures

Here is one way to represent the rules for significant figures:

Nonzero digits (26.3) are always significant.

(so 26.3 has three significant figures)


Significant figures143

Significant Figures

Here 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:


Significant figures144

Significant Figures

Here 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)


Significant figures145

Significant Figures

Here 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)


Significant figures146

Significant Figures

Here 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.


Significant figures147

Significant Figures

Here 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)


Significant figures148

Significant Figures

Here 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 figures149

Significant Figures

The only exception to those rules is when there is a line over a zero (630000).


Significant figures150

Significant Figures

The 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.


Significant figures151

Significant Figures

The 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.


Significant figures152

Significant Figures

The 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.

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.


  • Login