Chemistry 140 - CHAPTER 2-3
2000 lb =
1 ton
(7.0 x 10^-8) (2 x 10^5) =
1 x 10^-2
All measurements have:
1) number/value/magnitude 2) Unit [ex: miles, Fahrenheit, ft] 3) Errors
38.60 lb = ? g
1.751 x 10^4 g
Boiling point of water
100 degrees Celsius, 373 Kelvin, 212 degrees Fahrenheit
The uncertainty associated with the measured value 6.0230 × 10^3 is
10^-1
1 mm =
10^-3 m
1 mmol =
10^-3 mol
1 um =
10^-6 m
1 kg =
10^3 g
1Mb =
10^6 b
Your feisty neighbor Landy Ippert weighs 244 lb. What is his mass in kilograms?
111 kg
a x 10^b
a is coefficient; b is exponent/power
in a x 10^b
a is coefficient; b is exponent/power
Determine the number of significant figures in each of the following measured values. a. 2750 b. 2750.00 c. 675,000 d. 675.000
a) 3 b) 6 c) 3 d) 6
Express the following numbers in scientific notation. a. 0.0325 b. 345.00 c. 32,000 d. 97,000,300
a) 3.25 x 10^-2 b) 3.4500 x 10^2 c) 3.2 x 10^4 d) 9.70003 x 10^7
Label the following as a measurement or counted number & exact or inexact number a) 2 dozen roses b) 104 degrees fahrenheit c) 155 textbooks
a) counted; exact b) measurement; inexact c) counted; exact
C
degree celcius/Centigrade
the only difference in 560, 560. and 560.000000000000
diff error
example of measurement
distance like 5 miles
When rounding in conversion factor,
do NOT base rounding based on conversion factor.
a) Miranda: 577 people b) Alyssa: 574 people c) Brinley: 579 people d) Cassidy: 585 people e) Brianna: 581 people f) Brandi: 593 people An "electronic counter" indicates that 581 people passed through the gate in the designated time period. Which person's count is the most precise?
does not apply
If the first digit to be dropped is less than 5,
drop it & all digits following it w no change to last retained digit
If the first digit to be dropped is 5 or higher,
drop it & all digits that follow it AND increase value of last retained digit by 1.
53.78 miles
error is +/- 0.01
Estimated digit is where
error lies
No such thing as
exact measurement
Counted numbers are
exact numbers
Addition / Subtraction
final answer must have as many decimal places as measurement used in calculation w least number of decimal places
Multiplication / Division
final answer should have as many sig figs as measurement used in calculations w fewest sig figs
The correct answer obtained from adding the measurements 8.1, 3.14, and 97.143 contains
four significant figures
base unit for weight/mass
g [grams]
g x g x cm =
g^2cm
The calculated answer must be
given in correct number of sig figs based on measurements used in calculations.
Error or measurement is
going to give us precision of measurement w assumption that it is accurate
A measurement must
have a unit
The estimated digit(s) in the measured value 65,430 pounds is
the three
if set of data has large range of values,
then it's not precise
they're all close
then it's precise
When force of gravity acts on mass,
then its weight
Certain digits are all digits can read directly from instrument
there is marking for those digits
the zero in 560 is
trailing zero [no decimal point so insignificant]
Ex: 55005500, 0.00750300
trailing zeros
micro
u; 10^-6
Last digit we report is
uncertain digit [that's where error lies]
The last reported digit
uncertain digit which could change w instrument's precision
What is the difference in meaning between the times 3.3 seconds and 3.30 seconds?
uncertainty in first reading is ± 0.1 second & uncertainty in second reading is ± 0.01 second
It is the estimated digit where
uncertainty/error in precision lies
Unit 1 [conversion factor] =
unit 2
l =
v/wxh
Units are
very case sensitive.
cubic centimeter
volume
measurement =
way to quantify something
grams =
weight, mass
An exact number is a
whole number; it cannot possess decimal digits.
As long as using instrument,
will have uncertainty to measurement
Error is generally
written in between magnitude and unit.
There is
zero uncertainty when count something [it's exact number]
Temperature:
measure of hotness/coldness of substance
1.5 mile
measurement
200 V
measurement
25 L
measurement
3 cups
measurement
5 lbs
measurement
5.5 oz
measurement
55 degrees Fahrenheit
measurement
60 min
measurement
5 miles is
measurement bc can have errors [can be 4.99 miles]
Our skills of
measurements also introduce inaccuracies in measurements
Purpose of sig figs
tell us magnitude of error associated w measurement
25 books
counted number
555 children
counted number
Confined zeros are always
counted; significant
(1.5 x 10^12)/(9.222 x 10^-3) =
1.6 x 10^14
1 mi = _____ km
1.609 km
Convert the following to scientific notation: 16738
1.6738 x 10^4
(a x 10^y) + (b x 10^y) =
(a + b) x 10^y
(a x 10^y) - (b x 10^y) =
(a x 10^y) - (b x 10^y) = (a - b) x 10^y
(5.320 x 10^6) (0.32 x 10^3) =
1.7 x 10^9
In 560.00000000
+/- 0.00000001
Give the error in the following measurements 0.5600 g
+/- 0.0001
Give the error in the following measurements 0.560 g
+/- 0.001
Give the error in the following measurements 53.78 miles
+/- 0.01
Give the error in the following measurements 560 g
+/- 10
Absolute zero
-273 degrees Celsius, 0 Kelvin, -459.7 degrees Fahrenheit
Systems of Units:
-Metric System -English System
Convert the following to decimal notation: 3.65 x 10^-5
.0000365
Write 2.5 x 10^-4 in standard notation
.00025
Freezing point of water
0 degrees Celsius, 273 Kelvin, 32 degrees Fahrenheit
A blood analysis shows a vitamin-A concentration of 125 μmg/100mL of blood. How many grams of vitamin A are there in 1.2 L of this blood?
0.0015 g vitamin A
Which of the following represent the value "twenty-hundredths" written to two significant figures?
0.20
If a person's stomach produces 87 fl oz of gastric juice in a day, what is the equivalent volume of the gastric juice in gallons?
0.68 gal
1 qt = ____ L
0.9463 L
1 mL =
1 cm3 = 1 cc
12 in/1 ft or
1 ft/12 in
example of equivalence conversion factor
1 g water/1 mL water
density of water
1 g/mL
1 cm^3 =
1 mL = 1 cc
2 pints =
1 quart
32 fluid ounces =
1 quart
1 m = _____ yards
1.094 yards
An empty graduated cylinder has a mass of 42.817 g. When filled with 50.0 mL of an unknown liquid it has a mass of 106.773 g. What is the density of this liquid?
1.28 g/mL
Convert 5.0 x 10^4 cm^3 to gal
1.3 x 10^1 gal
Calculate the mass in lbs d = 1.11 g/mL v = 540,000 uL
1.32 lb
The amount of water in the world's oceans is estimated to be 1.35 × 10^9 km^3. What is this water volume in cubic centimeters?
1.35 x 10^24 cm^3
find the density if mass is 24,000 mg and volume is 0.0450 gal
1.4 x 10^-1 g/cc
A car travels at the speed of 89. 5 km/hr. What is the speed of this car in units of mi/s?
1.55 x 10^-2 mi/s
1 ft =
12 in
Standard equality example:
12 in = 1 ft
1237.6 + 23 + 0.12 =
1261
1 lb = ___ oz
16 oz
What is the uncertain digit in 4.82 lb
2
In 560, there are
2 sig figs [magnitude of error is +/- 10]
(6.97 x 10^-5) (2.45 x 10^4)(8.300 x 10^-2)/(7.2 x 10^-5) =
2.0 x 10^3
Write 226.0 in scientific notation
2.260 x 10^2
1 in =
2.54 cm
350.00 x 0.0075 =
2.6
1.5 ft x 1.5 ft x l = 1.5 gallon
2.7 cm
An aquarium (w = 1.5 ft, h = 1.5 ft) can hold 1.5 gallon of water when completely full. Calculate the length of this aquarium.
2.7 cm
(9.51167 x 10^-2)/(3.32 x 10^-3)
2.86 x 10^1
1 ton =
2000 lb
If aluminum metal is selling for 91.25 cents a pound, what would be the cost to a buyer, in dollars, who needs 2525 pounds of aluminum?
2304 dollars
3200[both zeros have overbar]0
4 sig figs
Using the dimensional analysis method of problem solving, set up and solve the following problem: "If your heart beats at a rate of 69 times per minute, how many times will your heart have beat by the time you reach your 8th birthday?" (Ignore the fact that two of the years were leap years.)
290,131,200 beats
1 yd =
3 ft
320[<- overbar]000
3 sig figs
If it is 560.
3 sig figs [zero is significant bc decimal]
3.111 - 3.11 + 3.1 =
3.1
3.73 x 10^2 = ? ft
3.11 x 10^1 ft
A certain chemical process consumes water at a rate of 55 L/sec. Express this water consumption rate in the following units. dL/min
3.3 x 10^4 dL/min
1.55 g/cc -> lb/L
3.42 lb/L
The ozone layer is a region in the upper atmosphere, at altitudes between 25 and 35 km, where the concentration of ozone is several times higher than at ground level. Express the altitude 35 km (the upper limit of the ozone layer) in centimeter units.
3.5 x 10^6 cm
A surface has an area of 365m^2 What is this area in each of the following units? km^2
3.65 x 10^-4 km^2
1 gal =____ L
3.785 L
Carry out the following multiplication, directly entering the numbers into a calculator in scientific notation. (4.72 × 10^−6) × (8.21 × 10^23)
3.88 x 10^18
Convert 3.89 mL to L
3.89 x 10^-3 L
2 cm x 5 cm x 3 cm =
30 cm^3
(5600 x 97.1)/(3.200 x 60) =
3000
Calculate the total mass of 130 text books if each weighs 2.351 lb.
305.6 lb
Round 3607.963 to 2 sig figs
3600
Round 3607.963 to 6 sig figs
3607.96
Round 3607.963 to 4 sig figs
3608
Round 3607.963 to 5 sig figs
3608.0
Round 3607.963 to 3 sig figs
3610
1 m = ___ in
39.37 in
you would have to multiple 130 books x 2.351 lbs = 305.63 BUT how many sig figs???
4 bc only count measurements [not exact numbers]
1 gal = ___ qt
4 qt
500 lb/in^2 -> mg/m^2
4 x 10^11 mg/m^2 ?
6.750 cm^3 -> in^3
4.119 x 10^-1 in^3
Convert the volume of 6.750 cm^3 to in^3.
4.119 x 10^-1 in^3
Convert the distance of 6.750 x 10^4 cm to miles.
4.195 x 10^-1 mi
In the example of bag of apples, which measurement is more accurate, 5 lb or 4.855 lb?
4.855 lb
Round 3607.963 to 1 sig fig
4000
1 lb = ____ g
453.6 g
4627 - 23.70 =
4603
What is the uncertain digit in 5 lb?
5
Example this example of uncertainty in measurements: A bag of apples from a grocery store
5 lb using balance at grocery store & 4.855 lb using more accurate balance in chem lab
Worldwide emissions of carbon dioxide into the atmosphere are estimated at 2 × 10^9 tons per year. What is this emission rate in pounds per hour?
5 x 10^8 lbs/hr
A vitamin-C tablet is found to contain 0.500 g of vitamin C. How many milligrams of vitamin C does this tablet contain?
5.00 x 10^2 mg
If see 503.63 x 10^4 , it would be fixed to
5.0363 x 10^6
Fix this: 5367.0 x 10^-8
5.3670 x 10^-5
0.0000555 x 10^-4
5.55 x 10^-9
5890 cm = ? km
5.89 x 10^-2 km
1 mi = ____ ft
5280 ft
67770.0/1250 =
54.2
A certain chemical process consumes water at the rate of 55 L/sec. How much water, in liters, is consumed in 3.0 hours?
590,000 L water
Convert the following to decimal notation: 5.920 x 10^3
5920
Convert the following to scientific notation: 6350370000
6.35037 x 10^9
A person is told that there are 60 seconds in a minute and also that a garden hose is 60 feet long. What is the fundamental difference between the value of 60 in these two pieces of information?
60 seconds in min is exact [defined] and 60 ft is measured [inexact]
Convert the following to decimal notation: 6.022 x 10^22
60220000000000000000000.
What is the uncertain digit in 4.817 lb
7
(3.780 x 10^-8)/(5.1 x 10^7) =
7.4 x 10^-16
Fix this: 0.00790 x 10^6
7.90 x 10^3
The average direct daily use of water in the United States per person is 3.0 × 10^5 mL. This includes water for drinking, cooking, bathing, dishwashing, laundry, flushing toilets, watering lawns, and so on. What is the volume, in gallons, of this amount of water?
79 gal
What is the uncertain digit in 4.8 lb
8
(5.32 x 10^8)(5.32 x 10^6)/(1.11 x 10^-5)(3 x 10^-4) =
8 x 10^23
Calculate the volume of air (in L) that will be present in a closed container with l = 55.5 in, w = 180 cm and h = 1.10 ft.
8.5 x 10^2 L
l= 55.5 in w = 180 cm h = 1.10 ft
8.5 x 10^2 L
Convert the following to scientific notation: 0.000000920
9.20 x 10^-7
Convert 5.80 x 10^3 mi to km.
9.33 x 10^3 km
Calculate the volume in gallons if m = 36.2 kg d = 0.9998 g/mL
9.57 gallons
a) Miranda: 577 people b) Alyssa: 574 people c) Brinley: 579 people d) Cassidy: 585 people e) Brianna: 581 people f) Brandi: 593 people An "electronic counter" indicates that 581 people passed through the gate in the designated time period. Which person's count is the most accurate?
Brianna's
K =
C + 273
Kelvin
K
C = (kelvin)
K - 273
mega
M; 10^6
Leading zeros are
NEVER sig figs
Exact numbers do
NOT affect sig figs in calculated answer
Temperature is
NOT energy [they are related]
when dividing
Numerator - denominator
Example: -have bag of apples. Weigh it twice. Same apples. Same measurer.
Only variable is instrument.
Dimensional Analysis is
Problem solving method to convert measurement from one unit to another for same property.
where the error lies
That's magnitude of error.
Dimensional Analysis:
Unit conversion
In 560.
There are 3 sig figs [+/- 1]
Given unit =
Unit 1
Desired/New unit =
Unit 2
In which of the following pairs of numbers do the two members of the pair have the same uncertainty? 3.102 and 5.134 0.20 and 0.200 301,000 and 300,000 more than one correct answer no correct response
a
F =
[1.8 x C] + 32
C = (fahrenheit]
[F - 32]/1.8
What is the magnitude of the uncertainty ( ±10 , ±0.1 , etc.) associated with each of the measured values in a. 3010.20 b. 0.00300300 c. 40,400 d. 33,000,000
a) +/- .01 b) +/- .00000001 c) +/- 100 d) +/- 1,000,000
What is the magnitude of the uncertainty associated with each of the following measured values? a. 2.31 b. 2.39 c. 2.376 d. 2.3003
a) +/- 0.01 b) +/- 0.01 c) +/- 0.001 d) +/- 0.0001
Without actually solving the problems, indicate the uncertainty (tenths, hundredths, etc.) that should be present in the answers to the following additions and subtractions. Assume that all numbers are measured quantities. a. 12.1 + 23.1 + 127.01 b. 43.65 - 23.7 c. 1237.6 + 23 + 0.12 d. 4650 + 25 + 200
a) +/- 0.1 b) +/- 0.1 c) +/- 1 d) +/- 100
What should the recorded uncertainty be ( ±0.1 unit, ± 0.01 unit, etc.) for measurements made using the following measuring-device scales. a. a thermometer scale with markings in 1 degree intervals b. a measuring cup scale with markings in 100 fluid ounce intervals c. a ruler scale with markings in 10 centimeter intervals d. a barometer scale with markings in 0.1 of a millimeter intervals
a) +/- 0.1 b) +/- 10 c) +/- 1 d) +/- 0.01
The monthly national sales volume for a particular automobile model was verbally reported as two hundred and five thousand units. What meaning, in terms of significant figures and magnitude of uncertainty, is conveyed by each of the following written notations for this number? a. 205,000 b. 205, 0[overbar]00 c. 205, 000. d. 205, 000 [overbar over last 3]
a) +/- 1,000 b) +/- 100 c) +/- 1 d) +/- 1
What is the uncertainty associated with each of the following measured values? a. 4.200 × 10^4 b. 4.2 × 10^5 c. 4.2 × 10^−1 d. 4.200 × 10^−3
a) +/- 10 b) +/- 10,000 c) +/- 0.001 d) +/- 0.000001
Identify the estimated digit in each of the measured values in a. 3010.20 b. 0.00300300 c. 40,400 d. 33,000,000
a) 0 b) 0 c) 4 d) 3
Round off each of the following measured numbers to three significant figures. a. 0.01234 b. 0.1257 c. 6.2374 d. 24.89
a) 0.0123 b) 0.126 c) 6.24 d) 24.9
Round off each of the following numbers to the number of significant figures indicated in parentheses. a. 0.350763 (three) b. 653.899 (four) c. 22.55555 (five) d. 0.277654 (four)
a) 0.351 b) 653.9 c) 22.556 d) 0.2777
A student determines that the mass of a 20.0 mL sample of olive oil (to be used in oil-and-vinegar salad dressing) is 18.4 g. a. What is the density of the olive oil in grams per milliliter? b. Predict whether the olive oil layer will be on the top or bottom in unshaken oil-and-vinegar salad dressing.
a) 0.920 g/mL b) olive oil bc density is less than water
Carry out the following multiplications and divisions, expressing your answers to the correct number of significant figures. Assume that all numbers are measured quantities. a. 3700 × 37.00 b. 4.2337 × 0.00706 c. 5671/4.44 d. 5.01/5.07
a) 1.4 x 10^5 b) 2.99 x 10^-2 c) 1.28 x 10^3 d) 9.88 x 10^-1
Perform the following computations, all of which involve multiplication and/or division. Express your answers to the proper number of significant figures. Assume that all numbers are measured quantities. a) 3.751 x 0.42 b) 1,810,000/3.1453 c) 1800.0/6.0000 d) (3.130 x 3.140)/3.15
a) 1.6 b) 5.75 x 10^5 c) 3.0000 x 10^2 d) 3.12
Carry out the following divisions in scientific notation. Be sure to take significant figures into account in obtaining your final answer. a) (2.05 x 10^-5)/(1.19 x 10^3) b) (3.92 x 10^10)/(9.1 x 10^-4)
a) 1.72 x 10^-8 b) 4.3 x 10^13
Without using a calculator, express in scientific notation the number in each of the following statements. a. Light travels at a speed of 186,000 miles per second. b. A person exhales approximately 320,000,000,000,000,000,000 molecules of carbon dioxide in one breath. c. The diameter of a human hair is 0.0016 inch. d. The maximum allowable amount of chromium in drinking water (EPA standard) is 0.00000010 gram per milliliter of water.
a) 1.86 x 10^5 b) 3.2 x 10^20 c) 1.6 x 10^-3 d) 1.0 x 10^-7
For the measured value 3.714 × 10^−3 Carry out the following uncertainty-related activities without using the decimal form of the number. a. Determine the uncertainty, expressed as a power of 10, associated with the measurement. b. Rewrite the measured value so that its uncertainty is increased by a factor of 100 (10^2). c. Rewrite the measured value so that its uncertainty is decreased by a factor of 100 (10^2). d. Rewrite the measured value so that its uncertainty is ± 10^−5
a) 10^-6 b) 10^-4 c) 10^-8 d) 3.71 x 10^-3
Write the name of the power of 10 associated with the listed metric system prefix or the metric system prefix associated with the listed power of 10. a. nano- b. micro- c. deci- d. 10^-2 e. 10^6 f. 10^9
a) 10^-9 b) 10^-6 c) 10^-1 d) centi e) mega f) giga
What is the uncertainty, in terms of a power of ten, associated with each of the following measured values? a) 3.700 x 10^4 b) 3.700 x 10^6 c) 3.70 x 10^5 d) 3.7 x 10^-2
a) 10^1 b) 10^3 c) 10^3 d) 10^-3
For a collection of identical 19.13 centimeter-long pencils, what would be the total combined length of the pencils if a. six pencils are present and the problem is solved using multiplication? b. six pencils are present and the problem is solved using addition? c. three pencils are present and the problem is solved using multiplication? d. three pencils are present and the problem is solved using addition?
a) 114.8 cm b) 114.78 cm c) 57.39 cm d) 57.39 cm
Perform the following additions or subtractions. Report your results to the proper number of significant figures. Assume that all numbers are measured quantities. a. 12 + 23 + 127 b. 3.111 + 3.11 + 3.1 c. 1237.6 + 23 + 0.12 d. 43.65 - 23.7
a) 162 b) 9.3 c) 1261 d) 20.0
Without actually solving the problems, indicate the number of significant figures that should be present in the answers to the following multiplications and divisions. Assume that all numbers are measured quantities. a. 4.5 × 4.05 × 4.50 b. 0.100 × 0.001 × 0.010 c. 655,000/6.5500 d. 6.00/33.000
a) 2 b) 1 c) 3 d) 3
For each of the following numbers, by how many places does the decimal point have to be moved in order to express the number in scientific notation? a. 0.0315 b. 0.00013 c. 3500 d. 63,003
a) 2 b) 4 c) 3 d) 4
How many digits will there be in the coefficient when each of the following numbers is expressed in scientific notation? a. 23 b. 23.000 c. 2300 d. 2300.000
a) 2 b) 5 c) 2 d) 7
An apple has a volume of 61cm^3. Express this volume in the following units. a) cubic feet b) cubic miles
a) 2.2 x 10^-3 ft^3 b) 4.7 x 10^-14 mi^3
Carry out the following multiplications involving scientific notation. Be sure to take into account significant figures in obtaining your final answer. a. (2.05 × 10^−3) × (1.19 × 10^−7) b. (7.92 × 10^10) × (1.19 ×10^−4)
a) 2.44 x 10^-10 b) 9.42 x 10^6
Perform the following mathematical operations, expressing your answers to the correct number of significant figures. Assume all numbers are measured quantities. a) 0.400 × (2.33 + 4.5) b) 0.300 × (3.73 + 3.0 + 2.777) c) 0.300 × (3.73 − 3.0) d) 0.650 × 7.23 × (6.772 + 3.10)
a) 2.7 b) 2.9 c) 0.2 d) 46.4
Using standard arithmetic notation and overbars (if needed), write the number 23,000 in a manner such that it has the following numbers of significant figures. a. two b. four c. six d. eight
a) 23, 000 b) 23, 0[overbar]0[overbar]0 c) 23, 000.0 d) 23, 000.000
What is the combined length, in inches, of eleven identical 2.21 inch metal rods when the problem is treated as ? a. a multiplication problem b. an addition problem
a) 24.3 in b) 24.31 in
Round off each of the following numbers to two significant figures. a. 25.7 b. 432,117 c. 0.435 d. 15,500
a) 26 b) 430,000 c) 0.44 d) 16,000
How many significant figures must the number Q possess, in each case, to make the following mathematical equations valid from a significant-figure standpoint? a. 7.312 × Q = 4.13 b. 7.312 × Q = 0.0022 c. 7.312 × Q = 20.44 d. 7.312 × Q = 0.1100
a) 3 b) 2 c) 4 or more d) 4 or more
Without actually doing any multiplications, indicate the number of significant figures that should be present in the answer to each of the following multiplications. Assume that all numbers are measured quantities. a. 6.00 × 6.00 × 6.00 b. 6.00 × 0.600 × 60.60 c. 0.006 × 0.060 × 0.600 d. 60,600 × 6060 × 606
a) 3 b) 3 c) 1 d) 3
Determine the number of significant figures in each of the following measured values. a. 2600 ±10 b. 1.375 ±0.001 c. 42 ±1 d. 73,000 ±1
a) 3 b) 4 c) 2 d) 5
How many significant figures does each of the following numbers have? a. 7770 b. 7.770 c. 7.770 × 10^−3 d. 7.770 × 10^3
a) 3 b) 4 c) 4 d) 4
Each of the following numbers is expressed in nonstandard (incorrect) scientific notation. Convert each number to standard (correct) scientific notation. a 342 × 10^4 b 23.6 × 10^−4 c 0.0032 × 10^5 d 0.12 × 10^−3
a) 3.42 x 10^6 b) 2.36 x 10^-3 c) 3.2 x 10^2 d) 1.2 x 10^-4
Rewrite the number 365,000 in scientific notation so that it fits each of the following specifications. a. has an uncertainty in the thousands place b. has an uncertainty in the tens place c. has an uncertainty in the tenths place d. has an uncertainty in the thousandths place
a) 3.65 x 10^5 b) b) 3.6500 x 10^5 c) 3.650000 x 10^5 d) 3.65000000 x 10^5
Carry out the following mathematical operations, expressing your answers to the correct number of significant figures. Assume that all numbers are measured quantities. a) (4.5 x 6.3)/7.22 b) (5.567 x 3.0001)/3.45 c) (37 x 43)/(4.2 x 6.0) d) (112 x 20)/(30 x 63)
a) 3.9 b) 4.84 c) 63 d) 1
A large flask contains 375 mL of strained (no seeds) watermelon juice. (Tests are to be run on the juice to see how much vitamin A it contains.) Specify the volume of this amount of juice in a. cubic centimeters. b. cubic feet.
a) 375 cm^3 b) 0.0132 ft^3
Perform the following computations, all of which involve addition or subtraction. Express your answers to the proper number of significant figures. Assume that all numbers are measured quantities. a) 13.01 + 13.001 + 13.010 b) 10.2 + 3.4 + 6.01 c) 0.6700 − 0.6644 d) 34.7 + 0.0007
a) 39.02 b) 19.6 c) 0.0056 d) 34.7
Determine the number of significant figures in the numerical value in each of the following statements. a. A wire has a diameter of 0.05082 inch. b. The mass of the earth is 6,600,000,000,000,000,000,000 tons. c. A hospital patient's blood glucose level was determined to be 4850 micrograms per milliliter of blood.
a) 4 b) 2 c) 3
Determine the number of significant figures in the following numbers assuming that each is a measurement: a) 300.0 b) 300. c) 300 d) 560. e) 560
a) 4 b) 3 c) 1 d) 3 e) 2
For each of the following numbers, how many significant figures should be present in the scientific notation form of the number? a. 27,520 b. 27.520 c. 0.001210 d. 1.37500
a) 4 b) 5 c) 4 d) 6
Carry out the following multiplications, making sure that your answer is expressed in correct scientific notation form and to the correct number of significant figures. a) (1.71 x 10^6) x (2.555 x 10^2) b) (5.37 x 10^-3) x (1.7 x 10^5) c) (9.0 x 10^-5) x (3.000 x 10^-5) d) (3.0 x 10^5) x (9.000 x 10^5)
a) 4.37 x 10^8 b) 9.1 x 10^2 c) 2.7 x 10^-9 d) 2.7 x 10^11
The number of people present at a parade was estimated by police to be 50,000. How many people were present at the parade if you assume that this estimate has each of the following uncertainties? a. 10,000 b. 1000 c. 100 d. 10
a) 40,000-60,000 b) 49,000-51,000 c) 49,900-50,100 d) 49,990-51,010
Round off each of the following measured values to three significant figures. a. 42,303 b. 42,360 c. 42,549 d. 42,601
a) 42, 300 b) 42, 400 c) 42, 500 d) 42, 600
Round off each of the following measured values to three significant figures. a. 42.55 b. 42.65 c. 42.75 d. 42.85
a) 42.6 b) 42.7 c) 42.8 d) 42.9
How many significant figures and what is the error in the following? a) 12.60 cm b) 125 feet c) 0.00000003 in d) 12.6 cm e) 500 L f) 500. L g) 500.0 L h) .0096 lb i) 70 mi/hr
a) 4; +/- .01 b) 3; +/- 1 c) 1; +/- 0.00000001 d) 3; +/- .1 e) 1; +/- 100 f) 3; +/- 1 g) 4; +/- .1 h) 2; +/- .0001 i) 1; +/- 10
A particular type of chemical balance is designed to display masses with an uncertainty of ±0.001 gram . How many significant figures should be reported when weighing samples with each of the following approximate masses on this balance? a. approximately 25 grams b. approximately 2 grams c. approximately 1 gram d. approximately 2/10 gram
a) 5 b) 4 c) 3 or 4 depending on if actual mass is greater or less than 1 d) 3
Determine the number of significant figures in each of the following measured values. a. 0.33333 b. 0.0003333 c. 0.303030 d. 0.00000003
a) 5 b) 4 c) 6 d) 1
Perform the following additions or subtractions with all numbers expressed in scientific notation. Answers will need to be checked for the correct number of significant figures and for the correct scientific notation form (coefficient is a number between 1 and 10). a) (2.661 x 10^3) + (3.011 x 10^3) b) (2.66 x 10^4) - (1.03 x 10^3) c) (9.98 x 10^-3) - (8.04 x 10^-5)
a) 5.672 x 10^3 b) 2.56 x 10^4 c) 9.90 x 10^-3
Without using a calculator, convert the scientific notation number in each of the following statements to a decimal number. a. The announced attendance at a football game was 5.3127 × 10^4 people. b. The circumference of the earth is 2.5 × 10^4 miles. c. The concentration of gold in seawater is 1.1 × 10^-8 gram per liter. d. The mass of a hydrogen atom is 1.67 × 10^-24 gram.
a) 53,127 b) 25,000 c) 0.000000011 d) 0.00000000000000000000000167
Determine the number of significant figures in the following numbers assuming that each is a measurement: a) 10200500000 b) 0.000300590 c) 15000 d) 15000. e) 90001 f) 0.0089000
a) 6 b) 6 c) 2 d) 5 e) 5 f) 5
Determine the number of significant figures in each of the following measured values. a. 3010.20 b. 0.00300300 c. 40,400 d. 33,000,000
a) 6 b) 6 c) 3 d) 2
Express each of the following numbers, to three significant figures, in scientific notation. a. 6666 b. 37.500 c. 0.34567 d. 1.3005
a) 6.67 x 10^3 b) 3.75 x 10^1 c) 3.46 x 10^-1 d) 1.30 x 10^0
Methane, a gas that is naturally present in the earth's atmosphere in small amounts, has a density of 0.714 g/L at a particular temperature and pressure. a. What is the mass, in grams, of 10.0 L of methane? b.What is the volume, in liters, of 10.0 g of methane?
a) 7.14 g b) 14.0 L
Perform the following additions or subtractions. Report your results to the proper number of significant figures. Assume that all numbers are measured quantities. a. 999.0 + 1.7 - 43.7 b. 345 - 6.7 + 4.33 c. 1200 + 43 + 7 d. 132 - 0.0073
a) 957.0 b) 343 c) 1300 d) 132
Label the following as a measurement or counted number & exact or inexact number a) 29 chairs b) 30 lb c) 555 pages in a book d) 555 mL water
a) counted; exact b) measurement; inexact c) counted; exact d) measurement; inexact
Label the following as a measurement or counted number & exact or inexact number a) 25 bananas b) 35 mi/hr c) 10 gallons of water
a) counted; exact b) measurement; inexact c) measurement; inexact
Indicate whether the number in each of the following statements is an exact or an inexact number. a. A classroom contains 24 chairs. b. There are 60 seconds in a minute. c. A bag of cherries weighs 4.1 pounds. d. A newspaper article contains 421 words.
a) exact b) exact c) inexact d) exact
Identify the metric system prefix corresponding to each of the following powers of ten. a. 10^-9 b. 10^6 c. 10^-3 d. 10^-1
a) nano b) mega c) milli d) deci
For each of the following numbers, will the exponent be positive, negative, or zero when the number is expressed in scientific notation? a. 0.0320 b. 321.7 c. 6.87 d. 63,002
a) negative b) positive c) zero d) positive
In the following pairs of numbers, tell whether both members of the pair contain the same number of significant figures. a. 11.0 and 11.00 b. 600.0 and 6.000 × 10^3 c. 6300 and 6.3 × 10^3 d. 0.300045 and 0.345000
a) no b) yes c) yes d) yes
Indicate whether each of the following metric system units is a unit of mass, volume, or length. a. kiloliter b. megagram c. micrometer d. centigram
a) volume b) mass c) length d) mass
In the following pairs of numbers, tell whether both members of the pair have an uncertainty of less than ± 0.01 . a. 0.006 and 0.016 b. 1.500 and 1.500 × 10^2 c. 3300.00 and 330[overbar]0[overbar] d. 5.750 × 10^1 and 5.750 × 10^−1
a) yes b) no c) no d) no
Indicate whether or not both members of each of the following pairs of measured values, when rounded to hundredths, contain the same number of significant figures. a. 24.736 and 24.766 b. 3.736 and 11.736 c. 0.06736 and 0.0111 d. 3.003 and 13.003
a) yes b) no c) yes d) no
tell whether both members of the pair have the same uncertainty. a. 11.01 and 11.00 b. 2002 and 2020 c. 0.05700 and 0.05070 d. 0.000066 and 660,000
a) yes b) no c) yes d) no
In the following pairs of numbers, tell whether both members of the pair contain the same number of significant figures. a. 11.01 and 11.00 b. 2002 and 2020 c. 0.05700 and 0.05070 d. 0.000066 and 660,000
a) yes b) no c) yes d) yes
What zeros are significant in the following examples? a) 12.202 km b) 0.01 mL c) 205 K d) 0.010 g e) 1000 mL f) 1000.0 mL g) .00850 gal
a) yes b) none c) yes d) last one e) none f) all g) last one
For the measured value 2.735 × 10^3 carry out the following uncertainty-related activities without using the decimal form of the number. a. Determine the uncertainty, expressed as a power of 10, associated with the measurement. b. Rewrite the measured value so that its uncertainty is increased by a factor of 100 (10^2) c. Rewrite the measured value so that its uncertainty is decreased by a factor of 1000 (10^−3) d. Rewrite the measured value so that its uncertainty is ± 10^3
a) ± 10^0 b) 2.7 × 10^3^ c) 2.735000 × 10^3 d) 3 × 10^3
(a x 10^y) (b x 10^z) =
a.b x 10^(y+z)
(a x 10y)/(b x 10z) =
a/b x 10^(y-z)
When is a measurement accurate?
accuracy depends on how close to true value
Significant figures =
all certain digits + one uncertain [estimated] digit
Certain digits are
all digits can read directly from instrument
Trailing Zeros:
all zeros after last non-zero digit
Leading Zeros
all zeros before first non-zero digit
Confined Zeros
all zeros between 2 non-zero digits
Measurements will
always have uncertainty/ambiguity bc no instrument can be 100% accurate
Measurements are
always inexact
all nonzero digits are
always sig figs
Sig figs in measurement
are ALWAYS IMPORTANT
The zeros in 3600 and 4000
are placeholders to maintain size of magnitude
1 L is defined as
area of cube of dimensions 10 cm
A prefix can be
attached to base unit of property being measured
Which of the following answers only contains one sig fig? a) 4.0 x (2.3 + 4.5) b) 3.0 x (3.7 - 3.4) c) 7.02 x (0.0001 + 0.011)
b
Measurement can only
be as exact as instrument allows it to be.
Certain digits must
be followed by ONE estimated digit
What's the saying?
be one with the prefix
The prefixes are written
before base unit of property.
if positive,
big number
in lab, we would like to achieve
both accuracy and precision
In which of the following measured numbers are all of the zeros significant? 0.000003140 360,031,010 3.0101 more than one correct response no correct response
c
In which of the following pairs of numbers do the two members of the pair have the same uncertainty? a) 480 x 10^5 and 4.80 x 10^6 b) 3.21 x 10^-4 and 3.2 x 10^-3 c) 3 x 10^-5 and 3.2211 x 10^-1
c
centi
c; 10^-2
the tool allows
certain amount of precision.
Example on graduated cylinder, can see 20 and 30
certainty is in tens place.
Ex: 130025, 0.09503
confined zeros
When the number 3009.1 is converted to scientific notation, the coefficient in the number
contains five significant figures
When problem has a per situation [example, 89.5 km/hr]
could mean 89.5 km/1 hr
12 eggs
counted number
13 potatoes
counted number
Precision
how close set of measurements on same object are to each other
The tool decides
how many sig figs
Each prefix
increases or decreases size of base unit by some factor of 10
Accuracy
indicates how close measurement [or average of set of measurements] is to true value
Precision is
indicator of reproducibility of data collected
560 means
it's between 550-570
560. means
it's between 559-560
If you count it,
it's counted number; NOT measurement [ex: 12 eggs, 5 cars]
kilo
k; 10^3
K
kelvin
Mass can be measured in
kilograms
grocery scale says 5 lbs. lab says 4.855 lb.
lab is more accurate [number of sig figs, decimal places means more accurate]
Unit
label for property being measured
In which digit in each measurement does the error lie?
last reported digit
Ex: 0.00032
leading zeros
Volume =
length x width x height
Uncertainty / error
lies in last reported sig fig
Every measurement is
limited by precision of instrument being used.
milli
m; 10^-3
Decimal only
matters for trailing zero
Measurements are like
measure BUT have to use a tool [like a ruler]
moles =
mol
Which of the following length measurements is consistent with a ruler that has subdivisions of 0.1 inch? 21.14 inches 21.1 inches 21.00 inches more than one correct response no correct response
more than one correct response
The coefficient
must be number between 1 and 10 [not including 10]
in scientific notation,
must have ONE non-zero digit before decimal point.
nano
n; 10^-9
If certainty is in tens place,
need 2 sig figs bc need certain digit(s) + estimated digit
Moving right,
negative
Power can be
negative or positive
Counted numbers are exact numbers
no errors
Conversion factors do
not affect sig figs in final answer.
Kelvin does
not have degree sign
25 books, 555 children, 12 eggs and 13 potatoes are
not measurements bc determined by counting & not by using instrument
For 12 eggs
not possible that there might have been 12.02 eggs
All leading zeros
not significant
All trailing zeros if no decimal point or overbar is present
not significant
Coefficient must be:
number between 1 and 10 [but can't be 10]
Scientific notation:
number multiplied by 10 raised to certain power
Addition/sub -
number of least decimal places.
Inexact number
number that has certain degree of uncertainty associated w it
Exact number
number that has no uncertainty/ambiguity about its value
Only base sig figs
on data given in original question.
When recording measurements using a reading instrument with calibrations
one MUST record all certain digits & ONE uncertain/estimated digit
ex: measure boiling point of water. If get 98 degrees Celsius. Someone else gets 75.
one closer to theoretical value is more accurate value
in sig fig context, if have 50 [overbar over 0]
overbar is always on trailing zeros to make it sig fig
Leading zeros act as
placeholders [tell us nothing about uncertainty]
Moving left,
positive
A student measures the mass of a metal object three times with the following results: 3.056 g, 3.057 g, and 3.056 g. Based on this information it is correct to say that the student's results are
precise
Error is always
present in place value of last reported sig fig
a) Miranda: 577 people b) Alyssa: 574 people c) Brinley: 579 people d) Cassidy: 585 people e) Brianna: 581 people f) Brandi: 593 people An "electronic counter" indicates that 581 people passed through the gate in the designated time period. (Team A is miranda, brinley and brianna. team B is alyssa, cassidy and brandi) Which team's count is the most precise?
team A
Measurement
quantities of properties of substance that are determined w use of instrument
Conversion factor is a
ratio derived from standard equality between unit 1 & 2 that allows for unit 1 to be cancelled & leave measurement in unit 2.
equivalence conversion factor
ratio that converts one type of measure to diff type of measure
use scientific notation for
really small or really big numbers.
Never forget to
record units
s
seconds
The calculator answer obtained from multiplying the measurements 42.44, 3.41, and 7.00 is 1013.0428. This answer
should be rounded to 1010
Trailing zero w overbar
sig fig
for multiplication,
sig figs number of fewest sig figs.
All confined zeros
significant
All non-zero digits
significant
All trailing zero if a decimal point or overbar is present
significant
if negative,
small number
Precision is when you
take set of measurements & all are within rounding of each other
a) Miranda: 577 people b) Alyssa: 574 people c) Brinley: 579 people d) Cassidy: 585 people e) Brianna: 581 people f) Brandi: 593 people An "electronic counter" indicates that 581 people passed through the gate in the designated time period. (Team A is miranda, brinley and brianna. team B is alyssa, cassidy and brandi) Which team's count is the most accurate?
team A
