answer each question completely. if asked to show your work, you will need to provide evidence for how you solved the problem, and include the requested information. 1. explain the difference between accuracy and precision. you may include a diagram or drawing with your explanation (5 points) 2. when we first studied division in this course, it was repeatedly stated that anything divided by itself is ______ (1 point) 3. for every equality in physics, there are always: (circle the correct answer) (1 point) a. three fudge factors b. three conversion factors c. two conversion factors d. two computer factors 4. for the equality 1000 mm = 1 m, write the conversion factors (4 points) 5. dimensional analysis is: (1 point) a. figuring out which dimension of the universe one is in. b. an unorganized way of doing physics problems c. a systematic approach to analyze the unit conversions in a physics problem. 6. if dimensional analysis is not utilized: (2 points) a. the units in the answer might not make sense b. the math computations might be incorrect c. there may be insufficient evidence to explain an answer d. all of the above e. none of the above

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Accepted Answer

### Question 1
# Brief Explanations:
Accuracy refers to how close a measured value is to the true or accepted value. For example, if the true weight of an object is 5 kg, and a scale measures it as 4.98 kg, that's accurate. Precision refers to how close multiple measured values are to each other, regardless of how close they are to the true value. For instance, if a scale repeatedly measures an object as 3.2 kg, 3.21 kg, 3.19 kg, it's precise (even if the true value is 5 kg). A diagram can be thought of as: for accuracy, darts clustered around the bullseye (true value); for precision, darts clustered tightly together (even if not near bullseye).
# Answer:
Accuracy is closeness to true value; Precision is closeness of measurements to each other.

### Question 2
# Explanation:
## Step1: Recall the division property
Any non - zero number $ a $ divided by itself ($ a\div a $) is equal to 1. We also consider the case when $ a = 0 $, but $ 0\div0 $ is undefined. In the context of basic division (usually non - zero numbers in introductory courses), anything (non - zero) divided by itself is 1.
# Answer:
1

### Question 3
# Brief Explanations:
In physics, for any equality (like $ 1\ m=100\ cm $), we can form two conversion factors. For example, from $ 1\ m = 100\ cm $, the conversion factors are $ \frac{1\ m}{100\ cm} $ and $ \frac{100\ cm}{1\ m} $. So for every equality, there are two conversion factors. Option a is incorrect (fudge factors are not related to basic equalities), option b is incorrect (not three), option d is incorrect (computer factors are irrelevant).
# Answer:
c. Two conversion factors

### Question 4
# Explanation:
## Step1: Recall conversion factor formation
Given the equality $ 1000\ mm = 1\ m $, a conversion factor is a fraction where the numerator and denominator are the two quantities from the equality.
## Step2: Form the first conversion factor
We can write $ \frac{1000\ mm}{1\ m} $. This is used when we want to convert meters to millimeters (multiplying by this factor will cancel out meters and give millimeters).
## Step3: Form the second conversion factor
We can also write $ \frac{1\ m}{1000\ mm} $. This is used when we want to convert millimeters to meters (multiplying by this factor will cancel out millimeters and give meters).
# Answer:
The conversion factors are $ \frac{1000\ \text{mm}}{1\ \text{m}} $ and $ \frac{1\ \text{m}}{1000\ \text{mm}} $

### Question 5
# Brief Explanations:
Dimensional analysis is a method used to check the consistency of physical equations and to perform unit conversions. Option a is incorrect (it has nothing to do with the dimension of the universe in a sci - fi sense). Option b is incorrect (it is an organized approach). Option c correctly describes dimensional analysis as a systematic way to analyze unit conversions in physics problems.
# Answer:
c. A systematic approach to analyze the unit conversions in a physics problem.

### Question 6
# Brief Explanations:
If we don't use dimensional analysis: the units in the answer might not make sense (for example, if we are calculating speed and end up with units of mass, that's wrong), the math computations might be incorrect (because we might have messed up the unit - related operations), and there may be insufficient evidence to explain an answer (since dimensional analysis helps in justifying the operations). So all of the above (option a, b, c) are correct, which means option d is correct.
# Answer:
d. All of the above

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Question 1

Step1: Recall the division property

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Question 2