1 1-6 Working with Numbers
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
1-6 Working with Numbers
2
Significant Digits (sig fig's) - Significant Digits (sig fig's) - certain digits and the estimated certain digits and the estimated digit of a measurement.digit of a measurement.
Rules of Sig Fig's (Atlantic-Pacific Rules of Sig Fig's (Atlantic-Pacific Rule)Rule)
3
P of pacific stands for decimal point present If a decimal point is present you If a decimal point is present you
start on the left side of the start on the left side of the number, like the pacific ocean is number, like the pacific ocean is on the left side of America. Read on the left side of America. Read through the number until you hit a through the number until you hit a non zero number. This begins the non zero number. This begins the significant numbers.significant numbers.
4
A of Atlantic stands for decimal point absent If the decimal point is absent you If the decimal point is absent you
begin counting all non-zero digits begin counting all non-zero digits from the right or Atlantic side of from the right or Atlantic side of the number.the number.
5
Significant Figures Rules Tablep.
p.
4747
6
Rule
s fo
r Sig
nifi
cant
Zero
s A
nim
ati
on
7
Examples
34.067g 34.067g 5 sig figs5 sig figs
0.0007458ml 0.0007458ml 4 sig figs 4 sig figs
0.009070g0.009070g 4 sig figs 4 sig figs
8
Examples
2030cm2030cm 3 sig figs3 sig figs
2007dm2007dm 4 sig figs4 sig figs
19,000,000,000g 19,000,000,000g 2 sig figs2 sig figs
9
Practice Problems
0.0026701m0.0026701m 5 sig figs5 sig figs
19.0550kg19.0550kg 6 sig figs6 sig figs
3500V3500V 2 sig figs2 sig figs
1,809,000L1,809,000L 4 sig figs 4 sig figs
10
Sig Fig's in Calculations
Exact numbers or conversions do not count Exact numbers or conversions do not count as sig figsas sig figs
In multiplication or division the answer can In multiplication or division the answer can only have as many sig figs as the number only have as many sig figs as the number with the least amount of sig figs.with the least amount of sig figs.
11
Example: Volume = length x width x height Find the volume an object 10.876m x Find the volume an object 10.876m x
1.34m x 13.22m1.34m x 13.22m on your calculator you will get a number on your calculator you will get a number
like 192.6661648like 192.6661648 The correct answer would be The correct answer would be
193m193m33
1.34m only has 3 sig figs1.34m only has 3 sig figs
12
In addition or subtraction the largest In addition or subtraction the largest uncertainty determines the number of sig uncertainty determines the number of sig figsfigs
13
Example
Add 34.50g + 3.2345g + 671.1g + 25.345g Add 34.50g + 3.2345g + 671.1g + 25.345g = 734.7745g= 734.7745g
The largest uncertainty is 0.1 The largest uncertainty is 0.1 therefore the answer could have therefore the answer could have one digit after the decimal. The one digit after the decimal. The correct answer would be 734.8g correct answer would be 734.8g after rounding upafter rounding up
14
Practice Problems
6.15m x 4.026m =6.15m x 4.026m = 12.7km / 3.0 =12.7km / 3.0 = 150ml + 76.9ml + 209ml + 0.036ml =150ml + 76.9ml + 209ml + 0.036ml = (35.6L + 2.4L) / 4.803 = (35.6L + 2.4L) / 4.803 = 2.542m x (16.408m - 3.88m) = 2.542m x (16.408m - 3.88m) =
15
Scientific Notation
M x 10M x 10nn
Greater than or equal to 1 but less than
10
A whole number
A negative exponent means the number is smallA positive exponent means the number is large
16
Scientific Notation
Example 19,000,000mlExample 19,000,000ml You can only have two sig fig'sYou can only have two sig fig's 1.9 x 101.9 x 1077
Example Example 0.0004569g 0.0004569g 3 sig figs 3 sig figs 4.57 x 104.57 x 10-4-4g g
17
Sample Problems
32,70032,700 3.27 x 103.27 x 1044
1,024,0001,024,000 1.024 x 101.024 x 1066
0.00471000.0047100 4.7100 x 104.7100 x 10-3-3
0.0000000039010.000000003901 3.901 x 103.901 x 10-9-9
18
Percent Error
% Error = % Error = measured – acceptedmeasured – accepted x 100 x 100
acceptedaccepted
19
Sample Problem
In class Friday we calculated the density of In class Friday we calculated the density of water. Many students reported values other water. Many students reported values other than the accepted value of 1g/ml or 1g/cmthan the accepted value of 1g/ml or 1g/cm33
Lets say you calculated the density of water Lets say you calculated the density of water to be .9g/mlto be .9g/ml
% Error =% Error = 0.9 - 1 0.9 - 1 x 100 = 10% error x 100 = 10% error
11
Chapter 2 Section 2 Units of Measurements pages 33-43
20
Density The ratio of mass to volumeThe ratio of mass to volume D = M / VD = M / V Unit = kg/mUnit = kg/m3 3 or g/cmor g/cm3 3 = g/mL= g/mL A characteristic physical propertyA characteristic physical property Can be used to identify a Can be used to identify a
substancesubstance Varies with temperatureVaries with temperature
Chapter 2 Section 2 Units of Measurements pages 33-43
21
Density Tablep.
38
p. 3
8
22
Densi
ty F
orm
ula
A
nim
ati
on
Chapter 2 Section 2 Units of Measurements pages 33-43
23
Density1.1. What is the density of a block of What is the density of a block of
marble that occupies 310 cmmarble that occupies 310 cm33 and and has a mass of 853 g?has a mass of 853 g?
2.2. Diamond has a density of 3.26g/cmDiamond has a density of 3.26g/cm33. . What is the mass of a diamond that What is the mass of a diamond that has a volume of 0.351 cmhas a volume of 0.351 cm33??
3.3. What is the volume of a sample of What is the volume of a sample of liquid mercury that has a mass of liquid mercury that has a mass of 76.2 g, given the density of mercury 76.2 g, given the density of mercury is 13.6 g/mL?is 13.6 g/mL?
p. 4
0
1. 2.75 g/cm3 2. 1.14 g 3. 5.60 mL
Related Documents
