Concept explainers
(a)
Interpretation:
The equivalency and both conversion factor a) hours and days is to be stated.
Concept introduction:
Equivalency is defined as the two quantities that are equivalent in value. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.
Answer to Problem 20E
The equivalency of a) hours and days is
Conversion factor of a) hours and days is given by;
Explanation of Solution
The two quantities that are equivalent in value is denoted as equivalence. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.
In the expression (1), the conversion factor 1 rod / 0.025 furlong is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of
A proportionality constant, m is inserted to convert a proportionality into an equality. Such as,
Given expression;
a) hours and days
Based on the above discussion the equivalency and conversion factors are states as follows;
The equivalency of a) hours and days is
Conversion factor of a) minutes and seconds is given by;
Thus, the equivalency and both conversion factor a) hours and days is stated.
(b)
Interpretation:
The equivalency and both conversion factor b) gallons and quarts is to be stated.
Concept introduction:
Equivalency is defined as the two quantities that are equivalent in value. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.
Answer to Problem 20E
The equivalency of b) gallons and quarts is
Conversion factor of b) gallons and quarts is given by;
Explanation of Solution
The two quantities that are equivalent in value is denoted as equivalence. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.
In the expression (1), the conversion factor 1 rod / 0.025 furlong is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of y = kx. Besides, the relationship is expressed as y α x. In the expression the symbol α is called as ‘is proportional to’.
A proportionality constant, m is inserted to convert a proportionality into an equality. Such as,
Given expression;
b) Gallons and quarts
Based on the above discussion the equivalency and conversion factors are states as follows;
The equivalency of b) gallons and quarts is
Conversion factor of b) gallons and quarts is given by;
Thus, the equivalency and both conversion factor b) gallons and quarts is stated.
Interpretation:
(c)
The equivalency and both conversion factor c) quarters and dollars is to be stated.
Concept introduction:
Equivalency is defined as the two quantities that are equivalent in value. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.
Answer to Problem 20E
The equivalency of c) quarters and dollars is
Conversion factor of c) quarters and dollars is given by;
Explanation of Solution
The two quantities that are equivalent in value is denoted as equivalence. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.
In the expression (1), the conversion factor 1 rod / 0.025 furlong is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of y = kx. Besides, the relationship is expressed as y α x. In the expression the symbol α is called as ‘is proportional to’.
A proportionality constant, m is inserted to convert a proportionality into an equality. Such as
Given expression;
c) quarters and dollars
Based on the above discussion the equivalency and conversion factors are states as follows;
The equivalency of c) quarters and dollars is
Conversion factor of c) quarters and dollars is given by;
Thus, the equivalency and both conversion factor c) quarters and dollars is stated.
Want to see more full solutions like this?
Chapter 3 Solutions
Bundle: Introductory Chemistry: An Active Learning Approach, 6th + LMS Integrated for OWLv2, 4 terms (24 months) Printed Access Card
- Write the equivalency and both conversion factors for each relationship: a Ten dimes is one dollar. b A football field is 100 yards long. c 16 ouncers is 1 pound.arrow_forwardWhich of the following statements use only exact numbers? (a) The temperature in our dorm room is kept at 72 F. (b) 1 bought 6 eggs, 2 cookies, and 5 tomatoes at the farmers' market. (c) There are 1109 nanometers in 1 meter.arrow_forwardWrite the equivalency and both conversion factors for each relationship: a A pack of gum is 9 pieces. b Two quarters are equal in value to five dimes. c One mile is 5280 feet.arrow_forward
- Which of the following quantities are expressed in metric units? a. The amount of aspirin in a tablet: 5grains b. The distance between two cities: 55km c. The internal displacement of an auto engine: 5L d. The time for a race: 4min, 5.2s e. The area of a field: 3.6acres f. The temperature on a hot day: 104Farrow_forwardWhich of the following quantities are expressed in metric units? a. Normal body temperature: 37C b. The amount of soft drink in a bottle: 2L c. The height of a ceiling in a room: 8.0ft d. The amount of aspirin in a tablet: 81mg e. The volume of a cooking pot: 4qt f. The time for a short race to be won: 10.2sarrow_forwardWrite the equivalency for each conversion factor: a)3feet1yardb)1meter100centimetersc)1milliliter20dropsarrow_forward
- Which of the following statements use only exact numbers? (a) The little boy weighs 74.3 lbs. (b) The boiling point of ethanol is 78C. (c) The mailman delivered 3 letters, 2 postcards and one magazine.arrow_forwardGive the two forms of the conversion factor that relate each of the following pairs of units. a. Days and hours b. Decades and centuries c. Feet and yards d. Quarts and gallonsarrow_forwardDetermine whether each statement that follows is true or false: a The SI system includes metric units. b If two quantities are expressed in an equivalency, they are directly proportional to each other. c The scientific notation form of a number smaller than 1 has a positive exponent. d In changing a number in scientific notation whose coefficient is not between 1 and 10 to standard scientific notation, the exponent becomes smaller if the decimal in the coefficient is moved to the right. e There are 1000 kilounits in a unit. f There are 10 milliunits in a centiunit g There are 1000 milliliters in a cubic centimeter. h The mass of an object is independent of its location in the universe. i Celsius degrees are smaller than Fahrenheit degrees. j The uncertain digit is the last digit written when a number is expressed properly in significant figures. k The quantity 76.2 g means the same as 76.200 g. l The number of significant figures in a sum may be more than the number of significant figures in any of the quantities added. m The number of significant figures in a difference may be fewer than the number of significant figures in any of the quantities subtracted. n The number of significant figures in a product may be more than the number of significant figures in any of the quantities multiplied. o The process of analysis of a problem statement includes describing the properties of the given and wanted quantities. p If the quantity in the answer to a problem is familiar, it is not necessary to check to make sure the answer is reasonable. q Conversion factors can be used to change from one unit to another only when the quantities are directly proportional. r When you are learning chemistry, you should check the solution to each problem you solve at two levels: 1 is the value reasonable? 2 what new knowledge or skill did I obtain or improve? s There is no advantage to using units in a problem that is solved by algebra. t A Fahrenheit temperature can be changed to a Celsius temperature by multiplying by a conversion factor.arrow_forward
- Use the following exact conversion factors to perform the stated calculations: 512 yd -= 1 rod 40 rods = 1 furlong 8 furlongs = 1 mile a. The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers? b. A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?arrow_forwardWrite conversion factors (as ratios) for the number of: kilometers in 1 mile liters in 1 cubic foot grams in 1 ouncearrow_forwardDistinguish precisely and in scientific terms the differences among items in each of the following groups. a Coefficient, exponent, exponential b Equivalency, conversion factor, quantity, value, unit c Analyze, identify, construct, check d Mass, weight e Unit, kilounit, centiunit, milliunit f Significant figures, uncertain digit g Uncertainty, exact number h The symbols = and i Fahrenheit, Celsius, kelvin j Direct proportionality, proportionality constant k Density, mass, volumearrow_forward
- Introductory Chemistry: An Active Learning Approa...ChemistryISBN:9781305079250Author:Mark S. Cracolice, Ed PetersPublisher:Cengage LearningGeneral, Organic, and Biological ChemistryChemistryISBN:9781285853918Author:H. Stephen StokerPublisher:Cengage LearningChemistry: Matter and ChangeChemistryISBN:9780078746376Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl WistromPublisher:Glencoe/McGraw-Hill School Pub Co
- Chemistry by OpenStax (2015-05-04)ChemistryISBN:9781938168390Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark BlaserPublisher:OpenStaxIntroductory Chemistry: A FoundationChemistryISBN:9781285199030Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningWorld of Chemistry, 3rd editionChemistryISBN:9781133109655Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCostePublisher:Brooks / Cole / Cengage Learning