Homework #1
HOMEWORK #1 Name ____________________________
- I. Convert the following numbers into scientific notation.
- II. Write the following numbers into expanded form.
- III. Indicate the number of significant figures for each of the following numbers.
- IV. Perform the following metric to metric conversion. Express the final answer in scientific notation with proper significant figures.
- 1.2 Measured Numbers and Significant Figures
- 1.4 Prefixes and Equalities
- 1.5 Problem Solving Using Conversion Factors
- Metric Conversion
- English System Conversions
- English-Metric Intersystem Conversions
- 1.6 Density
- 1.7 Temperature
- Temperature Conversions
- oC to K and K to oC
I. Convert the following numbers into scientific notation.
1. 43,200 2. 238,000
3. 0.567 4. 0.00308
II. Write the following numbers into expanded form.
1. 2.40x10^{1} 2. 2.8x10^{-3}
3. 4.24x10^{-5} 4. 7.923x10^{5}
III. Indicate the number of significant figures for each of the following numbers.
1. 0.00567 2. 13,500
3. 100.20 4. 0.00100
IV. Perform the following metric to metric conversion. Express the final answer in scientific notation with proper significant figures.
1. 10.6 cm = m
2. 450,000 mg = g
3. 12 mL = cL
4. 50 Mton = ton
5. 4,600 nm = mm
6. 0.058 kg = dg
7. 2460 mL = dL
8. 0.015 s = ms
9. 0.66 mm = mm
10. 0.062 g = cg
11. 12,500 cL = pt
12. 61,500 nm = in
13. 0.0520 kg = oz
14. 9,000 mL = oz
15. 1,989 mm = yd
1.1Units of Measurement
The Metric System - a “prefix-base unit” systems
Measurement | Metric Base Unit |
Length | Meter ( ) |
Volume | (L) |
Mass | ( ) |
Time | Second ( ) |
Temperature | Celsius (^{o}C) |
Scientific Notation - a simplified expression of numbers, which contains a single digit number and 10 to an exponent
Procedure:
1. Leave one digit to the left of the decimal point and write “x 10" after the number.
2. For numbers larger than one the power is positive, smaller than one it is negative .
3. Count the number of places the decimal point moves, this is the power of the ten.
Examples:
25000 0.00125
1.2 Measured Numbers and Significant Figures
Exact Numbers - obtained by counting items or from a two units in the same system
Measured Numbers - there is always some uncertainty in every measurement
Significant Figures- an indication of the accuracy of a measurement
Procedure (for determining which Zeroes are Significant):
1) All zeros at the end of a number are placement zeros
e.g.: 2500 (____ placement zeros, ____ S.F.)
2) All zeros before a number are placement
e.g.: 0.00125 (____ placement zero, ____ S.F.)
3) All zeros at the end of a number after the decimal are significant
e.g.: 0.0000430 (____ placement zero, ____ S.F.)
Example:
Write the following regular form numbers in scientific notation with proper significant figures:
4.50 50 1,250,000 0.001050
Wayne McGowan
Chem 110G
1.3 Significant figures in Calculations
Multiplication and Division:
The answer cannot have more significant figures (sig. fig.s) than the least no. of sig. fig.s used in the calculation.
Addition and Subtraction:
The answer should have the same number of decimal places as the measurement with the fewest decimal places.
1.4 Prefixes and Equalities
The special feature of the metric system is that a prefix can be attached to any base unit to increase or decrease its size by some factor of 10.
e.g.: a kilo anything is 1000 (10^{3}) anythings
1 kilometer (1 km) = 1000 meters (1000 m)
1 kiloliter (1 kL) = 1000 liters (1000 L)
1 kilogram (1 kg) = 1000 grams (1000 g)
Prefixes:
Prefix Abbr Numerical and Multiple
mega ........ M 1,000,000 = 1 x 10^{6}
kilo ........ k 1,000= 1 x 10^{3}
hecto h..... 100 = 1 x 10^{2}
deca ........ da 10 = 1 x 10^{1}
base unit (no prefix) 1
deci ........ d 0.1 = 1 x 10^{-1} = 1/10^{1}
centi ........ c 0.01 = 1 x 10^{-2} = 1/10^{2}
milli ........ m 0.001 = 1 x 10^{-3} = 1/10^{3}
micro m..... 0.000001 = 1 x 10^{-6} = 1/10^{6}
nano ........ n 0.000000001 = 1 x 10^{-9} = 1/10^{9}
1.5 Problem Solving Using Conversion Factors
Conversion Factors – the ratio of one unit to another
e.g.: 1 week = 7 days Þ
Unit Analysis (Dimensional Analysis / the Factor-Label Method) -the method used to perform the majority of all of the calculations in this class
Plan on learning and mastering it as soon as possible in order to make future calculations much easier. If you have problems understanding this procedure see me during my office hours as soon as possible.
This method is extremely helpful for all problems involving units. That is to say, if the problem has units we can use dimensional analysis to set it up and solve it (almost all scientific questions, and "real life" questions have units).
No knowledge of equations is involved, and neither is knowledge of algebra.
Procedure:
1) Identify the unit(s) of your answer and write it (them) down on the far right side of your paper where your answer will appear.
This step is of absolute importance, as it gives you a target to aim for, so that you will never get lost as to what you are after, and more importantly it tells you how to start the calculation. If your answer has a single unit then you will start with a single unit; if your answer has a compound unit (a "dual unit" e.g. m/hr) then you will start with either an already existing dual unit,or you will (most often) start with 2 separate single units, one above the other.
2) Identify the piece(s) of information that you start with and write it (them) down on the far left of your paper.
The answer’s unit(s) will tell you what kind of unit(s) you need. If you are starting with 2 separate units then the one on the top of the denominator line will lead you to the one on the top of your answers units, the one on the bottom leads you to the one on the bottom of your answers units.
3) Using available conversion factors cancel out of the beginning unit(s) and into a new unit that will be either the answers unit or a unit that gets you closer to the answers unit.
Most often there are several conversions that you will have to perform. Each conversion is done by putting the unit you want to convert out of on the opposite side of the denominator line and a unit that leads you to the desired unit on the same side of the denominator line. Using this procedure you will "walk" toward your answer.
4) Put in the numbers and then multiply the numerators (tops) and divide the denominators (bottoms) to get the final answer.
NOTE:Once you are done with setting up the problem all the unwanted units should cancel out leaving only the desired (answers) unit(s); then all that is left to do is to punch in the numbers on your calculator to get the answer.
Examples:
How many seconds are in 10.0 years? (in this problem you are expected to know the conversions, if you wouldn't know them they would be given in the problem)
How many miles will you have driven if you drive 1.25 miles per hour for 0.75 hours?
How far can you drive on 50 dollars of gas? Gas costs 0.899 dollars per gallon, and your car gets 35 miles per gallon and holds 15 gallons of gas.
What is the maximum number of friends that can be fed pizza if each friend eats 5 slices and you only have 50 dollars? At the pizzeria that you selected each pizza costs 12 dollars and has 8 slices?
My puppy walked 106 yards in 1.00 minutes, how fast did he walk in miles per hour?
How many 24 ounce cans of tomato sauce do you need to make enchiladas for a party of 34 people? You plan for each person eating 3 enchiladas and the recipe makes 12 enchiladas from 16 ounces of sauce.
NOTE: When setting up a problem using unit analysis you should be thinking only about the units and NOT about the numbers. Sometimes it may be helpful to wait to put the numbers in after the set up is complete.
Metric Conversion
Procedure:
1. write the unit to convert to on the far right
2. write the number and unit to convert from on the far left
3a. convert into the base unit write the equality to the base unit as a fraction with the base unit in the numerator and the given unit in the denominator
e.g.: to convert from mm to the base unit use
10^{-6} m
1 mm
3b. convert from the base unit to the wanted unit write the equality to the base unit as a fraction with the base unit in the denominator and the wanted unit as the numerator
e.g.: to convert from the base unit to mm use
1 nm
10^{-9} m
4. the equation is complete to compute quickly add all of the exponents in the numerator and subtract all of the exponents in the denominator
e.g.: convert 12,500 mm to nm
12,500 mm = 1.25x10^{4} mm 10^{-6}m 1 nm = 1.25x10^{[4+(-6)-{-9}]} =1.25x10^{7}nm
....... 1 mm 10^{-9}m
Examples:
Convert 37,400 nanometers to micrometers.
Convert 0.0072 kilograms to milligrams.
Convert 0.0849 milliliters to microliters.
Convert 4,712 kilobytes to megabytes.
English System Conversions
English-English Equivalents:
Volume ........ Length Mass _
1 gal = ___ qt.... 1 mi = _____ ft 1 s.ton = _____ lb
= ___ pt 1 yd = ____ ft 1 lb = ____ av.oz.
= ___ fl.oz. 1 ft = ____ in
Procedure:
1. write the unit to convert to on the far right
2. write the number and unit to convert from on the far left
3. place the unit you are trying to get out of across the denominator line and
the answers unit or one that gets you closer to the answer in the numerator
Examples:
convert 1500 ft into miles
1. ......... = miles
2. 1500 ft....... = miles
3. 1500 ft mile_ = miles
ft
4. 1500 ft 1 mile_ = 2.8x10^{-1} miles
5280 ft
How many inches are in 100 miles?
How many pints are in 32 fl.oz.?
English-Metric Intersystem Conversions
Metric-English Intersystem Equivalents:
Volume Length Mass _
1 L = _____ qt 1 m = _____ ft 1 lb = _____ g
NOTE:It is best to only use the conversions given above. That way you get used to and remember only one for each measurement type, and the ones above are for the metric base unit, which you always change into first anyway.
Procedure:
1. write the unit to convert to on the far right
2. write the number to convert from on the far left
3a. place the unit you are trying to get out of across the denominator line and the unit to be used in the intersystem conversion in the numerator
3b. use the intersystem conversion factor to convert into the other system
3c. convert from this unit to the wanted unit
4. put the numbers in and calculate
Example:convert 12.59 kilograms to ave.oz.
1. ......... = ave.oz.
2. 12.59 kg......... = ave.oz.
3. 12.59 kg g = ave.oz.
kg
3. 12.59 kg g Lb = ave.oz.
kg g
3. 12.59 kg g Lb ave.oz. = ave.oz.
kg g Lb
4. 12.59 kg10^{3} g 1 Lb 16 ave.oz. = 4.44x10^{2 }ave.oz.
1 kg 454 g 1 Lb
NOTE: The intersystem conversion terms have 3 significant figures.
How many pints are in 1725 mL?
How many centimeters are in 14 inches?
1.6 Density
Density is the ratio of a subject’s mass to its volume. Density units for the metric system are g/cc (cc = cubic centimeter) which is the standard for solids, liquids use g/mL and g/L are used for gasses.
To calculate the density of an object divide the mass by the volume and then convert by the normal method (dimensional analysis) into the units of choice.
Example:
127 lb of a rock sample displaces 18.5 qt of water, what is the rocks density?
What is the rocks density in g/ml ?
What is the density of a metal that displaces 1.17 L and has a mass of 16.82 kg?
43.2 Lb of a sample of sea water takes up 15.6 qt of space. What is the sample density?
Density as a conversion factor:
Any time you have a "dual unit" it can be used as a conversion factor. The dual unit miles/hour will work to take you from hours to miles, or from miles to hours. From density you have the conversion factor to take you from mass to volume, or from volume to mass.
e.g. g/ml will take you from milliliters to grams, or from grams to milliliters
Example:
How many pounds does 2.50 quarts weigh if its density is 1.105 g/ml?
What volume in gallons does 1.24 av.oz of a gas occupy if it has a density of 1.055 g/L ?
How many kg does a 3.618 L sample of alcohol weigh if it has a density of 0.772 g/mL?
How many dL does a 162 mg sample of gas occupy if it has a density of 1.14 g/L?
1.7 Temperature
The temperature of an object tells us how hot or cold that object is.
Kelvin Temperature Scale
Absolute zero has the value of ___ Kelvin. The Kelvin scale has no negative numbers.
Temperature Conversions
^{o}F to ^{o}C and ^{o}C to ^{o}F:
Fahrenheit has different size degrees from Celsius and the start point (0^{o}) is different.
To convert from ^{o}C to ^{o}F first multiply by 180 ^{o}F/100 ^{o}C and then add 32 ^{o}F.
To convert from ^{o}F to ^{o}C first subtract 32 ^{o}F and then multiply by 100 ^{o}C/180 ^{o}F.
^{o}C to K and K to ^{o}C
Centigrade/Celsius degrees are the same size as Kelvins, only 0 ^{o}C equals 273 Kelvins.
To convert from ^{o}C to K first multiply by 100 K/100 ^{o}C then add 273.
To convert from K to ^{o}C first subtract 273 and then multiply by 100 ^{o}C/100 K.
Examples:
34 ^{o}C = ......... = ^{o}F
55 ^{o}F = ......... = ^{o}C
25 ^{o}C = ........ = K (read 298 Kelvins, no degrees)
315 K = ......... = ^{o}C (read 42 degrees C)
What is the temperature in Celsius when it is 75 degrees Fahrenheit?
What is the temperature in Fahrenheit when it is 35 degrees Celsius?
What is the temperature in Kelvins when it is 35 degrees Celsius?
NOTE: Keep in mind that only identical units can be added or subtracted.