measurements reviewing main ideas 24. compare accuracy and precision. 25. a. write the equation that is used to calculate percentage error. b. under what condition will percentage error be negative? 26. how is the average for a set of values calculated? 27. what is meant by a mass measurement expressed in this form: 4.6 g ± 0.2 g? 28. suppose a graduated cylinder were not correctly calibrated. how would this affect the results of a measurement? how would it affect the results of a calculation using this measurement? 29. round each of the following measurements to the number of significant figures indicated. a. 67.029 g to three significant figures b. 0.15 l to one significant figure c. 52.8005 mg to five significant figures d. 3.174 97 mol to three significant figures 30. state the rules governing the number of significant figures that result from each of the following operations. a. addition and subtraction b. multiplication and division 31. what is the general form for writing numbers in scientific notation? 32. a. by using x and y, state the general equation for quantities that are directly proportional. b. for two directly proportional quantities, what happens to one variable when the other variable increases? 33. a. state the general equation for quantities, x and y, that are inversely proportional. b. for two inversely proportional quantities, what happens to one variable when the other increases? 34. arrange in the correct order the following four basic steps for finding the solution to a problem: check your work, analyze, solve, and plan.

Question

Accepted Answer

# 24.
# Brief Explanations:
Accuracy refers to how close a measurement is to the true or accepted value. Precision refers to how close a set of measurements of the same quantity are to one another. A measurement can be precise but not accurate, accurate but not precise, both, or neither.
# Answer:
Accuracy is closeness to true value; precision is closeness of repeated - measurements to each other.

# 25. a.
# Brief Explanations:
The formula for percentage error is $	ext{Percentage Error}=\frac{	ext{Experimental Value}-	ext{Theoretical Value}}{	ext{Theoretical Value}}	imes100\%$.
# Answer:
$	ext{Percentage Error}=\frac{	ext{Experimental Value}-	ext{Theoretical Value}}{	ext{Theoretical Value}}	imes100\%$

# 25. b.
# Brief Explanations:
Percentage error is negative when the experimental value is less than the theoretical value.
# Answer:
When the experimental value is less than the theoretical value.

# 26.
# Brief Explanations:
The average (arithmetic mean) of a set of values is calculated by summing all the values in the set and then dividing by the number of values in the set. Mathematically, if we have values $x_1,x_2,\cdots,x_n$, the average $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
# Answer:
Sum all values and divide by the number of values.

# 27.
# Brief Explanations:
The mass measurement $4.6\ g\pm0.2\ g$ means the actual mass is likely to be between $4.6 - 0.2=4.4\ g$ and $4.6 + 0.2 = 4.8\ g$. The $\pm0.2\ g$ represents the uncertainty or margin of error in the measurement.
# Answer:
The actual mass is in the range of $4.4\ g$ to $4.8\ g$; $0.2\ g$ is the uncertainty.

# 28.
# Brief Explanations:
If a graduated cylinder is not correctly calibrated, the measurement of volume will be inaccurate. When used in a calculation, any result that depends on that volume measurement will also be inaccurate. For example, if calculating density ($
ho=\frac{m}{V}$), an incorrect $V$ will give an incorrect $
ho$.
# Answer:
Measurement will be inaccurate; calculations using it will also be inaccurate.

# 29. a.
# Brief Explanations:
To round $67.029\ g$ to three significant figures, we look at the fourth - digit. Since $2<5$, we drop it.
# Answer:
$67.0\ g$

# 29. b.
# Brief Explanations:
To round $0.15\ L$ to one significant figure, we look at the second - digit. Since $5\geq5$, we round up the first digit.
# Answer:
$0.2\ L$

# 29. c.
# Brief Explanations:
$52.8005\ mg$ already has six significant figures. To round it to five significant figures, we look at the sixth - digit. Since $5\geq5$, we round up the fifth digit.
# Answer:
$52.801\ mg$

# 29. d.
# Brief Explanations:
To round $3.17497\ mol$ to three significant figures, we look at the fourth - digit. Since $4<5$, we drop it and the following digits.
# Answer:
$3.17\ mol$

# 30. a.
# Brief Explanations:
In addition and subtraction, the result should be rounded to the same number of decimal places as the measurement with the fewest decimal places.
# Answer:
Round to the same number of decimal places as the measurement with the fewest decimal places.

# 30. b.
# Brief Explanations:
In multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures.
# Answer:
Have the same number of significant figures as the measurement with the fewest significant figures.

# 31.
# Brief Explanations:
The general form for writing numbers in scientific notation is $a	imes10^{n}$, where $1\leq|a|<10$ and $n$ is an integer.
# Answer:
$a	imes10^{n}$, where $1\leq|a|<10$ and $n$ is an integer.

# 32. a.
# Brief Explanations:
The general equation for quantities $x$ and $y$ that are directly proportional is $y = kx$, where $k$ is the constant of proportionality.
# Answer:
$y = kx$

# 32. b.
# Brief Explanations:
For two directly proportional quantities, when one variable increases, the other variable also increases.
# Answer:
The other variable also increases.

# 33. a.
# Brief Explanations:
The general equation for quantities $x$ and $y$ that are inversely proportional is $xy=k$ or $y=\frac{k}{x}$, where $k$ is a non - zero constant.
# Answer:
$xy = k$ (or $y=\frac{k}{x}$)

# 33. b.
# Brief Explanations:
For two inversely proportional quantities, when one variable increases, the other variable decreases.
# Answer:
The other variable decreases.

# 34.
# Brief Explanations:
The correct order for solving a problem is analyze, plan, solve, and check your work. First, understand the problem (analyze), then develop a strategy (plan), execute the strategy (solve), and finally verify the solution (check).
# Answer:
Analyze, plan, solve, check your work.

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QUESTION IMAGE

Question

Explanation:

24.

Answer:

25. a.