1 / 25

What is the Length? - PowerPoint PPT Presentation

What is the Length?. We can see the markings between 1.6-1.7cm We can ’ t see the markings between the .6-.7 We must guess between .6 & .7 We record 1.67 cm as our measurement The last digit an 7 was our guess.. .stop there. Learning Check. What is the length of the wooden stick?

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about 'What is the Length?' - gualtier-meegan

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

• We can see the markings between 1.6-1.7cm

• We can’t see the markings between the .6-.7

• We must guess between .6 & .7

• We record 1.67 cm as our measurement

• The last digit an 7 was our guess...stop there

What is the length of the wooden stick?

1) 4.5 cm

2) 4.58 cm

3) 4.584 cm

Measurement and Significant Figures

• Every experimental measurement has a degree of uncertainty.

• The volume, V, at right is certain in the 10’s place, 10mL<V<20mL

• The 1’s digit is also certain, 17mL<V<18mL

• A best guess is needed for the tenths place.

• Why would we use scientific notation?

SCIENTIFIC NOTATION

A QUICK WAY TO WRITE

REALLY, REALLY BIG

OR

REALLY, REALLY SMALLNUMBERS.

• # from 1 to 9.999 x 10exponent

• 800 = 8 x 10 x 10

• = 8 x 102

• 2531 = 2.531 x 10 x 10 x 10

• = 2.531 x 103

• 0.0014 = 1.4 ÷ 10 ÷ 10 ÷ 10

• = 1.4 x 10-3

• To be in proper scientific notation the number must be written with

• * a number between 1 and 10

• * and multiplied by a power of

• ten

• 23 X 105 is not in proper scientific notation. Why?

0.0000187

370,000,000

78.8

0.02164

1.234 x 104

3.69 x 10–1

8 x 10–3

1.000 x 103

• Length meter m

• Mass kilogram kg

• Time second s

• Amount of substance mole mol

• Temperature Kelvin K

• Electric current amperes amps

• Luminous intensity candela cd

Quantity Name Symbol

Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16

• The International System of Units

• Derived Units Commonly Used in Chemistry

Map of the world where red represents countries whichdo not use the metric system

Power of 10 for

Prefix Symbol Meaning Scientific Notation

_________________________________________________________

mega- M 1,000,000 106

kilo- k 1,000 103

deci- d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro-m 0.000001 10-6

nano- n 0.000000001 10-9

pico- p 0.000000000001 10-12

Digits

Uncertain

Digit

Significant figures

• Method used to express accuracy and precision.

• You can’t report numbers better than the method used to measure them.

• 67.20 cm = four significant figures

???

• The number of significant digits is independent of the decimal point.

• 255

• 31.7

• 5.60

• 0.934

• 0.0150

These numbers

All have three

significant figures!

• Every non-zero digit is ALWAYS significant!

• Zeros are what will give you a headache!

• They are used/misused all of the time.

• SEE p.24 in your book!

0.421 - three significant figures

Captive zeros

114.20 - five significant figures

Trailing zero

Rules for zeros

???

• Captive zeros are always significant!

???

Trailing zeros are significant …

IF there’s a decimal point in the number!

???

• 250 mg

• \__ 2 significant figures

• 120. miles

• \__ 3 significant figures

• 0.00230 kg

• \__ 3 significant figures

• 23,600.01 s

• \__ 7 significant figures

Significant figures:Rules for zeros

• Scientific notation - can be used to clearly express significant figures.

• A properly written number in scientific notation always has the proper number of significant figures.

0.00321 = 3.21 x 10-3

Three Significant

Figures

• An answer can’t have more significant figures than the quantities used to produce it.

• Example

• How fast did you run if you

• went 1.0 km in 3.0 minutes?

0.333333

speed = 1.0 km

3.0 min

= 0.33 km

min

ONLY 2 SIG FIGS!

Significant figures and calculations

• Multiplication and division.

• Your answer should have the same number of sig figs as the original number with the smallest number of significant figures.

21.4 cm x 3.095768 cm = 66.2 cm2

135 km ÷ 2.0 hr = 68 km/hr

+ 234.11 g

357.57 g

805.4 g

- 721.67912 g

83.7 g

Significant figures and calculations

• Your answer should have the same number of digits to the right of the decimal point as the number having the fewest to start with.

• After calculations, you may need to round off.

• If the first insignificant digit is 5 or more, you round up

• If the first insignificant digit is 4 or less, you round down.

If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then -

2.5795035 becomes 2.580

34.204221 becomes 34.20

1st insignificant digit

• For example you want a 4 Sig Fig number

0 is dropped, it is <5

8 is dropped, it is >5; Note you must include the 0’s

5 is dropped it is = 5; note you need a 4 Sig Fig

4965.03

780,582

1999.5

4965

780,600

2000.

49.7

46.4

.05985

1.586 107

1.000

32.27  1.54 = 49.6958

3.68  .07925 = 46.4353312

1.750  .0342000 = 0.05985

3.2650106 4.858 = 1.586137  107

6.0221023 1.66110-24= 1.000000