The Measurements and Units project is designed to:
(1.) Meet one of the learning objectives of the VCCS (Virginia Community College System) standards for:
MTH 111: Basic Technical Mathematics
(Provides a foundation in mathematics with emphasis in arithmetic, unit conversion, basic algebra, geometry and trigonometry.).
MTH 130: Fundamentals of Reasoning
(Presents elementary concepts of algebra, linear graphing, financial literacy, descriptive statistics, and measurement & geometry. ).
MTH 131: Technical Mathematics
(Presents algebra through unit conversion, trigonometry, vectors, geometry, and complex numbers.).
MTH 133: Mathematics for Health Professions
(Presents in context the arithmetic of fractions and decimals, the metric system and dimensional analysis, percents, ratio and proportion, linear equations, topics in statistics, topics in geometry, logarithms, topics in health professions including dosages, dilutions and IV flow rates.).
MTH 154: Quantitative Reasoning
[Solve reallife problems requiring interpretation and comparison of various representations of ratios (i.e., fractions, decimals, rates, and percentages including part to part and part to whole, per capita data, growth and decay via absolute and relative change)].
(2.) Meet the QM (Quality Matters) and USDOE (United States Department of Education) requirements for distance education as regards the
provision of RSI (Regular and Substantive Interaction).
Federal Register: Distance Education and Innovation
St. John's University: New Federal Requirements for Distance Education: Regular and Substantive Interaction (RSI)
Student – Content Interaction: Very high
Student – Student Interaction: Flexible
Student – Faculty Interaction: Flexible
(3.) Convert between International Metric System of units and United States Customary System of units.
Skills Measured/Acquired
(1.) Use of prior knowledge
(2.) Critical Thinking
(3.) Interdisciplinary connections/applications
(4.) Technology
(5.) Active participation through direct questioning
(6.) Research
(1.) This is an individual project.
It is not a group project.
Students may work together. However, each student must submit his/her/their own project.
(2.) The items only allowed in the project include containers of:
(a.) Food (includes fruits)
(b.) Drinks (excluding alcoholic drinks)
(c.) Soaps
(d.) Lotion
(e.) Paint
If you are unsure whether any container is permitted, please ask the Professor accordingly.
(3.) The image of the container used must be included.
Please use the Insert → Pictures icon to insert the image directly.
The image should be very clear.
(4.) Please use only the three tables given to you.
The use of any other table will lead to major deduction of points.
The three tables are:
Prefix  Symbol  Multiplication Factor 

yocto  y  $10^{24}$ 
zepto  z  $10^{21}$ 
atto  a  $10^{18}$ 
femto  f  $10^{15}$ 
pico  p  $10^{12}$ 
nano  n  $10^{9}$ 
micro  $\mu$  $10^{6}$ 
milli  m  $10^{3}$ 
centi  c  $10^{2}$ 
deci  d  $10^{1}$ 
deka  da  $10^1$ 
hecto  h  $10^2$ 
kilo  K  $10^3$ 
mega  M  $10^6$ 
giga  G  $10^9$ 
tera  T  $10^{12}$ 
peta  P  $10^{15}$ 
exa  E  $10^{18}$ 
zetta  Z  $10^{21}$ 
yotta  Y  $10^{24}$ 
Measurement  Customary  Customary  Unit Conversion Factor 

Length  inch (in)  foot (ft)  $12\:inches = 1\:ft$ 
Length  foot (ft)  yard (yd)  $3\:ft = 1\:yd$ 
Length  yard (yd)  mile (mi)  $1760\:yd = 1\:mi$ 
Length  foot (ft)  mile (mi)  $5280\:ft = 1\:mi$ 
Length  rod/pole  yards (yd)  $1\:rod = 5.5\:yd$ 
Length  furlong  rod  $1\:furlong = 40\;rod$ 
Length  fathom  feet (ft)  $1\:fathom = 6\;ft$ 
Length  league/marine  nautical miles  $1\:league = 3\;nautical\;\;miles$ 
Mass  pound (lb)  ounce (oz)  $1\:lb = 16\:oz$ 
Mass  short ton (ton)  pound (lb)  $1\:short\:ton = 2000\:lb$ 
Mass  long ton  pound (lb)  $1\:long\:ton = 2240\:lb$ 
Mass  stone  pound (lb)  $1\:\:stone = 14\:lb$ 
Mass  long ton  stone  $1\:long\:ton = 160\:stones$ 
Area  acre (acre)  square feet ($ft^2$)  $1\:acre = 43560\:ft^2$ 
Volume  quart (qt)  pint (pt)  $1\:qt = 2\:pt$ 
Volume  pint (pt)  cup (cup)  $1\:pt = 2\:cups$ 
Volume  quart (qt)  cup (cup)  $1\:qt = 4\:cups$ 
Volume  quart (qt)  fluid ounce (fl. oz)  $1\:qt = 32\:fl.\:oz$ 
Volume  pint (pt)  fluid ounce (fl. oz)  $1\:pt = 16\:fl.\:oz$ 
Volume  cup (cup)  fluid ounce (fl. oz)  $1\:cup = 8\:fl.\:oz$ 
Volume  gallon (gal)  quart (qt)  $1\:gal = 4\:qt$ 
Volume  gallon (gal)  quart (pt)  $1\:gal = 8\:pt$ 
Volume  gallon (gal)  cup (cup)  $1\:gal = 16\:cups$ 
Volume  gallon (gal)  fluid ounce (fl. oz)  $1\:gal = 128\:fl.\:oz$ 
Volume  gallon (gal)  cubic inches ($in^3$)  $1\:gal = 231\:in^3$ 
Measurement  Metric  Customary  Unit Conversion Factor 

Length  meter (m)  foot (ft)  $1\:ft = 0.3048\:m$ 
Length  kilometer (km)  nautical miles  $1\:nautical\;\;miles = 1.852\;km$ 
Mass  gram (g)  pound (lb)  $1\:lb = 453.59237\:g$ 
Mass  metric ton (tonne)  kilogram (kg)  $1\:tonne = 1000\:kg$ 
Volume 
liter or cubic decimeters (L or $dm^3$) 
gallons (gal)  $1\:L = 0.26417205\:gal$ 
(5.) As a student, you have free access to Microsoft Office suite of apps.
(a.) Please download the desktop apps of Microsoft Office on your desktop/laptop (Windows and/or Mac only).
Do not use a chromebook.
Do not use a tablet/iPad.
Do not use a smartphone.
Do not use the web app/sharepoint access of Microsoft Office.
(Please contact the IT/Tech Support for assistance if you do not know how to download the desktop app.)
In that regard, the project is to be typed using the desktop version/app of Microsoft Office Word only.
(b.) The file name for the Microsoft Office Word project should be saved as: firstName–lastName–project
Use only hyphens between your first name and your last name; and between your last name and the word, project.
No spaces.
(c.) For all English terms/work (entire project): use Times New Roman; font size of 14; line spacing of 1.5.
Further, please make sure you have appropriate spacing between each heading and/or section as applicable.
Your work should be wellformatted and visually appealing.
(d.) For all Math terms/work: symbols, variables, numbers, formulas, expressions, equations and fractions among others,
the Math Equation Editor is required.
(i.) The font is set to Cambria Math by default (set it to that font if it is not); font size of 14, and
align accordingly (preferably leftaligned).
(ii.) To ensure appropriate spacing between your Math work, use a line spacing of 2.0.
Alternatively, you may use line spacing of 1.5 but insert a space after each equation as applicable.
Your work should be wellformatted, organized, wellspaced (not compact), and visually appealing.
(e.) Include page numbers. You may include at the top of the pages or at the bottom of the pages but not both.
(6.) All work must be shown.
If you use any variables, please define your variables accordingly.
You may use any or a combination of the 3 methods taught/discussed:
(a.) First Method: Unity Fraction Method
(b.) Second Method: Proportional Reasoning Method
(c.) Third Method: Fast Proportional Reasoning Method
If you do not want to use any of these method, you are welcome to use any other preapproved appropriate method.
(7.) Please ensure your answer matches the converted quantity and unit on the container you used.
Do not approximate intermediate calculations.
If the converted quantity on the container was rounded:
(a.) First, write your answer as is (exact value)
(b.) Second, round accordingly to match the converted quantity on the container. (approximate value)
(c.) Third, specify the type of rounding that was done (how many decimal places, how many significant digits, etc.)
(8.) (a.) Please review the examples I did.
You may not do the same examples that I did.
These are the minimum expectations.
Creativity is always welcome.
NOTE: I did the conversion of one unit to another unit (customary unit to metric unit).
However, please make sure you do two conversions: customary unit to metric unit; and metric unit to customary unit.
(b.) Please review the samples from my previous students also.
You may not submit any of their containers.
(c.) References were not required in previous projects.
However, as at 05/09/2024, references are required, going forward.
It is important to cite your references in any academic paper.
(9.) Mr. C (SamDom For Peace) wants you to do this realworld project very well.
Hence, he highly recommends that you submit a draft so he can give you feedback.
(a.) First: (Required): Please submit a clear image of the entire container in the Projects: Containers page in the Canvas course.
The clear image of the entire container should clearly show the units on the container.
I shall review and respond.
(b.) Second: (Highly Recommended): When your container is approved, please submit your draft.
Draft projects are not graded because they are drafts. They are only for feedback.
If your professor gives you an opportunity to submit a draft, please use that opportunity.
Submitting drafts is highly recommended. Submitting drafts is not required.
It is highly recommended because I want to give you the opportunity to do your project very well and make an excellent
grade in it.
Please turn in your draft in the Discussions page → Projects: Drafts forum in the Canvas course
(if you would like your colleagues to read my comments and avoid any mistakes that you made).
You may also send it to me via email (if you do not want your colleagues to see my comments and learn from the comments).
I shall review and provide feedback.
Then, review my feedback and make changes as necessary.
Keep working with me until I give you the green light to turn in your actual project. This must be done before
the final due date to turn in the actual project.
When everything is fine (after you make changes as applicable based on my feedback), please submit your
work in the appropriate area: Assignments page → Measurements and Units Project in the Canvas course.
Only the projects submitted in the appropriate place in the Canvas course are graded.
(10.) All work must be turned in by the final due date to receive credit.
Please note the due dates listed in the course syllabus for the submission of the draft and the actual project.
In the course syllabus, we have the:
(a.) Initial due date for the Project Draft: Please turn in your draft.
(b.) Initial due date for the Project: If your draft is not ready for submission, keep working with me. Make changes
based on my feedback and keep working with me until I give you the green light to turn it in.
If you prefer not to turn in a draft, please review all the resources provided for you and do your project well and
submit.
(c.) Final due date for the Project Draft: This is necessary if you want a written feedback for your draft.
After this date, written feedback would not be provided for your draft. However, verbal feedback would still be provided
during Office Hours/Student Engagement Hours/Live Sessions.
(d.) Final due date for the Project: All work must be turned in by this date to receive credit.
After this date, no work may be accepted.
Name:  (Registered name as is in the Canvas course) 
Instructor:  Samuel Chukwuemeka 
Objective:  To convert a measurement from a unit to another unit. 
Measurement:  Mass 
1st: Given Unit:  Customary unit (Ounce) 
To Convert to:  Metric unit (Gram) 
2nd: Given Unit:  Metric unit (Gram) 
To Convert to:  Customary unit (Ounce) 
Container Used:  Soap (Please see the bottom left corner.) 


Calculations:  
References: (New addition. Not in previous Student Projects.) 
Cite your source(s) accordingly. Indicate the type of citation format. 
Convert $4.25\:oz$ to $g$
From Given Tables:
$
1\:lb = 16\:oz \\[3ex]
1\:lb = 453.59237\:g \\[3ex]
1\:lb = 1\:lb \\[3ex]
\implies 16\:oz = 453.59237\:g \\[3ex]
Let\:\:p = mass\:\:of\:\:4.25\:oz\:\:in\:\:g \\[3ex]
\underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex]
$
$oz$  $g$ 

$16$  $453.59237$ 
$4.25$  $p$ 
$ \dfrac{p}{4.25} = \dfrac{453.59237}{16} \\[5ex] Multiply\:\:both\:\:sides\:\:by\:\:4.25 \\[3ex] 4.25 * \dfrac{p}{4.25} = 4.25 * \dfrac{453.59237}{16} \\[5ex] p = \dfrac{4.25 * 453.59237}{16} \\[5ex] p = \dfrac{1927.76757}{16} \\[5ex] p = 120.485473 \\[3ex] p \approx 120\:g...rounded\:\:to\:\:the\:\:nearest\:\:whole\:\:number \\[3ex] \therefore 4.25\:oz \approx 120\:g \\[3ex] $ This confirms the quantity in $g$ (in parenthesis) in the soap container.
Name:  (Registered name as is in the Canvas course) 
Instructor:  Samuel Chukwuemeka 
Objective:  To convert a measurement from a unit to another unit. 
Measurement:  Volume 
1st: Given Unit:  Customary unit (Fluid Ounce) 
To Convert to:  Metric unit (Milliliters) 
2nd: Given Unit:  Metric unit (Milliliters) 
To Convert to:  Customary unit (Fluid Ounce) 
Container Used:  Water (Please see the top center corner.) 

Convert $16.9\:fl\:\:oz$ to $mL$
From Given Tables:
$
1\:L = 0.26417205\:gal \\[3ex]
1\:gal = 4\:qt \\[3ex]
1\:qt = 4\:cups \\[3ex]
1\:cup = 8\:fl.\:oz \\[3ex]
$
Based on what we were given:
Let us first convert it to liters ($L$)
Then, we will convert from liters ($L$) to milliliters ($mL$)
$
\underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex]
16.9\:fl\:oz\:\:to\:\:L \\[3ex]
Set\:\:it\:\:up\:\:and\:\:check\:\:to\:\:make\:\:sure\:\:it\:\:is\:\:correct \\[3ex]
16.9\:fl\:oz * \dfrac{.....L}{.....gal} * \dfrac{.....gal}{.....qt} * \dfrac{.....qt}{.....cup} * \dfrac{.....cup}{.....fl.\:oz} \\[5ex]
16.9\:fl\:oz * \dfrac{1\:L}{0.26417205\:gal} * \dfrac{1\:gal}{4\:qt} * \dfrac{1\:qt}{4\:cup} * \dfrac{1\:cup}{8\:fl.\:oz} \\[5ex]
= \dfrac{16.9 * 1 * 1 * 1 * 1}{0.26417205 * 4 * 4 * 8} \\[5ex]
= \dfrac{16.9}{33.8140224} \\[5ex]
= 0.4997926541\:L \\[3ex]
Convert\:\:0.4997926541\:L\:\:to\:\:mL \\[3ex]
\underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex]
Set\:\:it\:\:up\:\:and\:\:check\:\:to\:\:make\:\:sure\:\:it\:\:is\:\:correct \\[3ex]
0.4997926541\:L * \dfrac{.....mL}{.....L} \\[5ex]
= 0.4997926541\:L * \dfrac{1\:mL}{10^{3}\:L} \\[5ex]
= 0.4997926541\:L * \dfrac{1\:mL}{0.001\:L} \\[5ex]
= 499.7926541\:mL \\[3ex]
499.7926541\:mL \approx 500\:mL \\[3ex]
$
This confirms the quantity in $mL$ in the water container.
Student: Sir, you could have used the direct conversion from gallons to cups...
and bypass quarts
$
16.9\:fl\:oz * \dfrac{.....L}{.....gal} * \dfrac{.....gal}{.....cup} * \dfrac{.....cup}{.....fl.\:oz} \\[5ex]
16.9\:fl\:oz * \dfrac{1\:L}{0.26417205\:gal} * \dfrac{1\:gal}{16\:cups} * \dfrac{1\:cup}{8\:fl.\:oz} \\[5ex]
$
Teacher: That is right!
You are correct.
But, what if you were given a table that does not have that direct conversion?
Student: Then, I would use what I was given.
But, in this case; we were given that direct conversion.
Name:  (Registered name as is in the Canvas course) 
Instructor:  Samuel Chukwuemeka 
Objective:  To convert a measurement from a unit to another unit. 
Measurement:  Lengths (Width by Length) 
1st: Given Unit:  Customary unit (in by in) 
To Convert to:  Metric unit (cm by cm) 
2nd: Given Unit:  Metric unit (cm by cm) 
To Convert to:  Customary unit (in by in) 
Container Used:  Hand Wipes (Please see the bottom center corner.) 

Convert $5.7\:in\:\:by\:\:7.5\:in$ to $cm\:\:by\:\:cm$
$
Width = 5.7\:in \\[3ex]
Length = 7.5\:in \\[3ex]
$
From Given Tables:
$
1\:ft = 0.3048\:m \\[3ex]
12\:inches = 1\:ft \\[3ex]
1\:ft = 12\:inches \\[3ex]
1\:ft = 1\:ft \\[3ex]
\implies 0.3048\:m = 12\:inches \\[3ex]
$
We shall use the First Method to convert the width.
We shall use the Second Method to convert the length.
Use any method(s) you prefer.
$
\underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex]
Convert\:\:the\:\:Width \\[3ex]
5.7\:in \:\:to\:\: cm \\[3ex]
Set\:\:it\:\:up\:\:and\:\:check\:\:to\:\:make\:\:sure\:\:it\:\:is\:\:correct \\[3ex]
5.7\:in * \dfrac{.....m}{.....in} * \dfrac{.....cm}{.....m} \\[5ex]
5.7\:in * \dfrac{0.3048\:m}{12\:in} * \dfrac{1\:cm}{10^{2}\:m} \\[5ex]
= 5.7\:in * \dfrac{0.3048\:m}{12\:in} * \dfrac{1\:cm}{0.01\:m} \\[5ex]
= \dfrac{5.7 * 0.3048 * 1}{12 * 0.01} \\[5ex]
= \dfrac{1.73736}{0.12} \\[5ex]
= 14.478\:cm \approx 14.5\:cm \\[3ex]
\underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex]
Convert\:\:the\:\:Length \\[3ex]
Let\:\:p = length\:\:of\:\:7.5\:in\:\:in\:\:m \\[3ex]
Let\:\:c = length\:\:of\:\:p\:m\:\:in\:\:cm \\[3ex]
$
Based on what we were given:
We need to first convert to meters ($m$)
Then, we will convert from meters ($m$) to centimeters ($cm$)
From Given Tables:
$
1\:ft = 0.3048\:m \\[3ex]
12\:inches = 1\:ft \\[3ex]
1\:ft = 12\:inches \\[3ex]
1\:ft = 1\:ft \\[3ex]
\implies 0.3048\:m = 12\:inches \\[3ex]
1\:cm = 10^{2}\:m \\[3ex]
1\:cm = 0.01\:m
$
$in$  $m$ 

$12$  $0.3048$ 
$7.5$  $p$ 
$m$  $cm$ 

$0.01$  $1$ 
$0.1905$  $c$ 
The results confirm the quantities in cm in the hand wipe container.
Chukwuemeka, S.D (2016, April 30). Samuel Chukwuemeka Tutorials  Math, Science, and Technology.
Retrieved from https://quantitativereasoning.appspot.com/
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Bennett, J. O., & Briggs, W. L. (2023). Using and Understanding Mathematics: A Quantitative Reasoning Approach. Pearson.
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