Module 6 Practice
- Page ID
- 237179
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Theory and Law
Exercise \(\PageIndex{1}\)
Tell whether each statement is most similar to a hypothesis, observation, theory, or law.
This box of cereal is less expensive than that one.
- Answer
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observation
The larger the box of cereal, the lower the price per ounce is.
- Answer
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law
If I buy the largest package of food I can eat before it goes stale, I will save money on groceries.
- Answer
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hypothesis
The cost associated with packaging plays an important role in setting the price of groceries. For the size of the packaging, the cost does not increase proportionally to the volume. Therefore, the fraction of the price that is going towards packaging is smaller for larger sizes.
- Answer
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theory
Extensive and Intensive Properties
Exercise \(\PageIndex{1}\)
Tell whether each is an extensive or intensive property.
(a) length
(b) mass
(c) temperature
(d) the weight of a piece of clay
(e) the color of the clay
(f) the price of a bunch of apples
(g) the price per pound of the apples
- Answer (a)
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Extensive
- Answer (b)
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Extensive
- Answer (c)
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Intensive
- Answer (d)
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Extensive
- Answer (e)
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Intensive
- Answer (f)
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Extensive
- Answer (g)
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Intensive
Exact and Measured Numbers
Exercise \(\PageIndex{1}\)
Tell whether each number represents an exact number or an uncertain, measured number.
I have 12 coins.
- Answer
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Exact
The total mass of my coins is 27.420 g.
- Answer
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Uncertain (measured)
The average mass of each coin is therefore 2.2850 g per coin.
- Answer
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Uncertain (measured)
One of the metals used to make the coins is nickel, which has a density of 8.908 g/cm3.
- Answer
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Uncertain (measured)
The prefix "kilo" means 1000, so there are 1000 g in a kg.
- Answer
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Exact
That means the total mass of my coins is 0.027420 kg.
- Answer
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Uncertain (measured)
Precision and Accuracy
Exercise \(\PageIndex{1}\)
You used a calibration mass to test three balances. The mass is 25.000 g. Your results are below.
| Balance A | Balance B | Balance C | |
| Trial 1 | 24.81 g | 24.97 g | 24.57 g |
| Trial 2 | 24.69 g | 25.28 g | 24.69 g |
| Trial 3 | 24.93 g | 24.93 g | 24.63 g |
| Trial 4 | 25.09 g | 25.06 g | 24.66 g |
| Trial 5 | 25.33 g | 25.11 g | 24.55 g |
| Average | 24.97 g | 25.07 g | 24.62 g |
| Standard Deviation | 0.25 g | 0.14 g | 0.06 g |
Which balance is the most precise?
- Answer
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Balance C. (It has the lowest standard deviation. The trials are closest together.)
Which balance is the least precise?
- Answer
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Balance A.
Which balance is the most accurate?
- Answer
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Balance A. (The average value is closest to 25.000 g)
Which balance is the least accurate?
- Answer
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Balance C.
What is the percent error of balance B? (Use the average measurement to calculate.)
- Answer
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0.3 %.