Chapter 2: Measurements and Calculations
Scientific Notation
Main Concepts:
*The objective of scientific notation is the represent how very large or very small a number is. It can be expressed as the product of a number between 1 and 10 and a power of 10.
*The numbers associated with scientific notation are often very large or very small; therefor, scientific notation makes it easier to represent these numbers.
*For example, the distance from the Earth to the Moon is a large number that would be extremely bulky, so with scientific notation it makes it compact and easier to write.
Calculations:
*The objective of scientific notation is the represent how very large or very small a number is. It can be expressed as the product of a number between 1 and 10 and a power of 10.
*The numbers associated with scientific notation are often very large or very small; therefor, scientific notation makes it easier to represent these numbers.
*For example, the distance from the Earth to the Moon is a large number that would be extremely bulky, so with scientific notation it makes it compact and easier to write.
Calculations:
Video:
http://www.youtube.com/watch?v=i6lfVUp5RW8
*This video explains the process you go through to write a number into scientific notation along with a faster way of doing it.
Website:
http://www.mathsisfun.com/numbers/scientific-notation.html
*This website helps again to re-inforce the method of scientific notation when expressing really large or really small numbers. It even has a space where you can plug in a number and practice yourself.
http://www.youtube.com/watch?v=i6lfVUp5RW8
*This video explains the process you go through to write a number into scientific notation along with a faster way of doing it.
Website:
http://www.mathsisfun.com/numbers/scientific-notation.html
*This website helps again to re-inforce the method of scientific notation when expressing really large or really small numbers. It even has a space where you can plug in a number and practice yourself.
Types of Units:
Main Concepts:
*There are two types of units: SI and US units. The US units are based off of the English System and SI are based off of the Metric System.
*Units: important because they show the scale or standard that is being used to express the number/measurement.
-Volume: the amount of three dimensional space occupied by an object (measured in liters: L)
-Mass: the quantity of matter in an object (measured in grams: G)
-Significant figures: numbers recorded in a measurement
Website:
http://physics.nist.gov/cuu/Units/
*This website shows you the different SI units along with the prefixes that go with them. It explains rules and also gives you background information on the units and the system that goes along with them.
Converting Between Different SI Units:
Main points:
*When converting between SI units, the base has a unit and then the following units follow a patten as to how to relate it to the original unit it is in. Units are a part of measurement that tell us what scale is being used to represent the result of a measurement. A measurement is a quantitative observation because it deals with numbers. SI units are based on and deprived from the Metric System.*The goal for this section to understand converting different unit from one step to multi step conversion.
Remember You must Always use some conversion factor.
http://www.chartsgraphsdiagrams.com/miscellaneous/unit-conversions.html
*This website explains how to convert from one SI unit to another.
Activity:
http://www.sciencegeek.net/Chemistry/taters/Unit0Metrics.htm
*This website helps to re-inforce converting between SI units and lets you do practice problems with the conversions.
Video:
http://www.youtube.com/watch?v=E21EFW1e3d4
*This video gives examples of converting problems. It works it out step by step and explains what must be done in order to go about the correct way in finding the answer. It shows multistep problems when there is no direct conversion.
Conversion:
20Mm times 1x10^6 m times 1km times 1 mi equals 12,422.36025 mi
1Mm 1x10^-3m 1.61 km
So: the 'Mm' from the given and then the conversion from 'M' to 'm' will cancel out the "M" and then the "m" will be divided out when you convert from 'm' to 'km'. Then 'km' will be divided out when it is converted to 'mi' leaving your final answer in 'mi' and then you can go back and plug it into your calculator to get the right answer in the correct unit.
Uncertainty In Measurement
Main Concepts:
*Every measurement has an uncertainty which is due to the sensitivity of the instruments or the ability of the user when measuring something.
Website:
http://physics.nist.gov/cgi-bin/cuu/Info/Uncertainty/index.html
*This website shows the essentials of expressing the uncertainty of a specific measurement that you get.
Video:
http://www.youtube.com/watch?v=CmVIxfV7t7g
*This video shows what uncertainty and where it comes from by doing an example on the board and explaining it step by step to make it easy to understand.
Significant Figures:
Main Concepts:
*The numbers recorded in a measurement
Rules of Sig Figs:
Rules
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html
*This website talks about the rules for significant figures and what you do to figure out how many are needed for certain problems.
Video:
http://www.youtube.com/watch?v=5UjwJ9PIUvE
*This video explains significant figures and how to solve for them. It shows an example so that you can visualize what it should look like and what steps to take in order to find the correct number of significant figures to include in your answers.
Temperature Scales:
Main Concepts:
*The quantity that tells how hot or cold:
-Temperature can be measured in degrees Celsius or degrees Fahrenheit.
-Nearly all Matter expands when its temperature increases and contracts when its temperature decreases.
-Kelvin - calibrated in terms of energy. Absolute zero is the point at which there is NO kinetic energy.
Activity:
http://nova.stanford.edu/projects/mod-x/ad-tempscales.html
*This activity will give you an idea of the different temperature scales. It will also allow you to practice converting between the scales.
Website:
http://lamar.colostate.edu/~hillger/temps.htm
*This website shows you the three different scales. It shows the comparisons and baseline temps. in each scale.
Video:
http://www.youtube.com/watch?v=FjdscyVkSBA
*This video shows how to convert between the Celsius, Fahrenheit, and Kelvin scales. It shows the 2 formulas you need to remember in order to convert between the scales.
Calculation:
number 1: 25.6 degrees F to degrees C
25.6 degrees F= 1.80(C) + 32
*subtract 32 from both sides*
6.4 = 1.80(C)
*divide by 1.80 on both sides*
3.5555555556= C
C= 3.66
answer: 3.66 degrees C
number 2: 45 degrees C to K
K= 273.15 + 45
K= 318.15
answer: 318.15 K
Density:
Main Concepts:
*The masses of the atoms and the spacing between them determines density
Density is the measure of the relative "heaviness" of objects with a constant volume.
-Density can be expressed in terms of mass.
-Amount of mass per unit volume
-Density equals mass/volume
-Measured in g/cm(to the 3rd power) or g/ml
Activity:
http://www.spacegrant.hawaii.edu/class_acts/Density.html
*This activity will help understand the compactness of planetary matter by measuring mass and volume and relating these to density.
Website:
http://www.elmhurst.edu/~chm/vchembook/120Adensity.html
*This website will help to better explain what density is and how to find it.
Video:
http://www.youtube.com/watch?v=7tVebi3TSsg
*This video helps to show how to solve for density by doing practice problems showing each step.
Calculation:
****formula: d=m/v****
*problem 1:
m= 234g
v= 90mL
so... 234g/90mL
d= 2.6g/mL
*problem 2:
m= 75.4g
v= 5.24cm^3
so... 75.4g/5.24cm^3
d= 14.4g/cm^3
Main Concepts:
*There are two types of units: SI and US units. The US units are based off of the English System and SI are based off of the Metric System.
*Units: important because they show the scale or standard that is being used to express the number/measurement.
-Volume: the amount of three dimensional space occupied by an object (measured in liters: L)
-Mass: the quantity of matter in an object (measured in grams: G)
-Significant figures: numbers recorded in a measurement
Website:
http://physics.nist.gov/cuu/Units/
*This website shows you the different SI units along with the prefixes that go with them. It explains rules and also gives you background information on the units and the system that goes along with them.
Converting Between Different SI Units:
Main points:
*When converting between SI units, the base has a unit and then the following units follow a patten as to how to relate it to the original unit it is in. Units are a part of measurement that tell us what scale is being used to represent the result of a measurement. A measurement is a quantitative observation because it deals with numbers. SI units are based on and deprived from the Metric System.*The goal for this section to understand converting different unit from one step to multi step conversion.
Remember You must Always use some conversion factor.
- Conversion factor- a ratio of the two part of the statement that relates to two units
- Example: 1 in. equals 2. 54 cm
http://www.chartsgraphsdiagrams.com/miscellaneous/unit-conversions.html
*This website explains how to convert from one SI unit to another.
Activity:
http://www.sciencegeek.net/Chemistry/taters/Unit0Metrics.htm
*This website helps to re-inforce converting between SI units and lets you do practice problems with the conversions.
Video:
http://www.youtube.com/watch?v=E21EFW1e3d4
*This video gives examples of converting problems. It works it out step by step and explains what must be done in order to go about the correct way in finding the answer. It shows multistep problems when there is no direct conversion.
Conversion:
20Mm times 1x10^6 m times 1km times 1 mi equals 12,422.36025 mi
1Mm 1x10^-3m 1.61 km
So: the 'Mm' from the given and then the conversion from 'M' to 'm' will cancel out the "M" and then the "m" will be divided out when you convert from 'm' to 'km'. Then 'km' will be divided out when it is converted to 'mi' leaving your final answer in 'mi' and then you can go back and plug it into your calculator to get the right answer in the correct unit.
Uncertainty In Measurement
Main Concepts:
*Every measurement has an uncertainty which is due to the sensitivity of the instruments or the ability of the user when measuring something.
Website:
http://physics.nist.gov/cgi-bin/cuu/Info/Uncertainty/index.html
*This website shows the essentials of expressing the uncertainty of a specific measurement that you get.
Video:
http://www.youtube.com/watch?v=CmVIxfV7t7g
*This video shows what uncertainty and where it comes from by doing an example on the board and explaining it step by step to make it easy to understand.
Significant Figures:
Main Concepts:
*The numbers recorded in a measurement
Rules of Sig Figs:
- 1- Nonzero integers are always significant (1,2,3,4, etc)
- 2- Three classes of zeros
- A. Leading zeros are never counted as significant
- Leading zeros are zeros that precedes all of the nonzero digits
- example 0.0033mi. (2 Significant figures)
- B. Captive zeros are always count as significant figures.
- Captive zeros are zeros that fall between nonzero digits
- Example 150.01 m/s. (5 Significant figures)
- C. Trailing(tailing) zeros are only significant with a decimal place.
- Trailing zeros are zeros at the right end of the number
- Example. 144000. m (6 Significant figures)
- 3-Exact numbers
- -calculation involved with counting has unlimited significant figures.
Rules
- If the digit is to be removed
- A. is less then 5, the preceding digit stays the same.
- Ex. 5. 13 rounds to 5. 1
- B. is equal or greater than 5, the preceding digit is increased by 1.
- Ex. 3. 16 rounds to 3. 2
- DO NOT ROUND UNTIL THE FINAL ANSWER
- For multiplication or division.
- Identify the number with the lowest significant figure and the final answer will have the same number of significant figures.
- Example: 4. 98763542009 x 3. 3
- Equals: 16. 45919689
- Final answer is 16. 5
- Addition or subtraction
- The limiting term is the one with the smallest number of decimal places.
- Remember, the last digit reported in a measurement is actually an uncertain number.
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html
*This website talks about the rules for significant figures and what you do to figure out how many are needed for certain problems.
Video:
http://www.youtube.com/watch?v=5UjwJ9PIUvE
*This video explains significant figures and how to solve for them. It shows an example so that you can visualize what it should look like and what steps to take in order to find the correct number of significant figures to include in your answers.
Temperature Scales:
Main Concepts:
*The quantity that tells how hot or cold:
-Temperature can be measured in degrees Celsius or degrees Fahrenheit.
-Nearly all Matter expands when its temperature increases and contracts when its temperature decreases.
-Kelvin - calibrated in terms of energy. Absolute zero is the point at which there is NO kinetic energy.
Activity:
http://nova.stanford.edu/projects/mod-x/ad-tempscales.html
*This activity will give you an idea of the different temperature scales. It will also allow you to practice converting between the scales.
Website:
http://lamar.colostate.edu/~hillger/temps.htm
*This website shows you the three different scales. It shows the comparisons and baseline temps. in each scale.
Video:
http://www.youtube.com/watch?v=FjdscyVkSBA
*This video shows how to convert between the Celsius, Fahrenheit, and Kelvin scales. It shows the 2 formulas you need to remember in order to convert between the scales.
Calculation:
number 1: 25.6 degrees F to degrees C
25.6 degrees F= 1.80(C) + 32
*subtract 32 from both sides*
6.4 = 1.80(C)
*divide by 1.80 on both sides*
3.5555555556= C
C= 3.66
answer: 3.66 degrees C
number 2: 45 degrees C to K
K= 273.15 + 45
K= 318.15
answer: 318.15 K
Density:
Main Concepts:
*The masses of the atoms and the spacing between them determines density
Density is the measure of the relative "heaviness" of objects with a constant volume.
-Density can be expressed in terms of mass.
-Amount of mass per unit volume
-Density equals mass/volume
-Measured in g/cm(to the 3rd power) or g/ml
Activity:
http://www.spacegrant.hawaii.edu/class_acts/Density.html
*This activity will help understand the compactness of planetary matter by measuring mass and volume and relating these to density.
Website:
http://www.elmhurst.edu/~chm/vchembook/120Adensity.html
*This website will help to better explain what density is and how to find it.
Video:
http://www.youtube.com/watch?v=7tVebi3TSsg
*This video helps to show how to solve for density by doing practice problems showing each step.
Calculation:
****formula: d=m/v****
*problem 1:
m= 234g
v= 90mL
so... 234g/90mL
d= 2.6g/mL
*problem 2:
m= 75.4g
v= 5.24cm^3
so... 75.4g/5.24cm^3
d= 14.4g/cm^3