Two students need to determine the density of iron for part of an experiment. Using the information in the table below, calculate the average of each student's trials. Which student has the most precise set of measurements? Which student's average is the most accurate?
data table of Sarah and Felipe's measurements
Question 2 options:
Felipe's measurements are more precise but Sarah's average is more accurate.
Sarah's measurements are more precise but Felipe's average is more accurate.
Felipe's measurements are more precise and his average is more accurate.
Sarah's measurements are more precise and her average is more accurate.
To determine which student has the most precise set of measurements, we need to compare the range of their trials. Range is a measure of how spread out the measurements are.
For Sarah's measurements, the range is 0.9 g/cm³ (1.5 - 0.6).
For Felipe's measurements, the range is 0.4 g/cm³ (1.7 - 1.3).
Since the range is smaller for Felipe's measurements, we can conclude that Felipe has the most precise set of measurements.
To determine which student's average is the most accurate, we need to compare their averages with the known density of iron. The known density of iron is 7.87 g/cm³.
For Sarah's average, the deviation from the known density is 0.4 g/cm³ (7.6 - 7.87).
For Felipe's average, the deviation from the known density is 0.13 g/cm³ (7.74 - 7.87).
Since the deviation is smaller for Felipe's average, we can conclude that Felipe's average is more accurate.
Therefore, the correct answer is: Felipe's measurements are more precise and his average is more accurate.
The accepted value for the boiling point of water is 100˚C. During an experiment, students recorded the temperature observations listed below. Which one is the most accurate temperature for the boiling point of water?
To determine which temperature observation is the most accurate for the boiling point of water, we need to compare each observation to the accepted value of 100˚C.
Temperature observations:
1. 97˚C
2. 99˚C
3. 101˚C
4. 98˚C
5. 100.5˚C
To determine the accuracy, we calculate the deviation of each observation from the accepted value:
1. Deviation = 97˚C - 100˚C = -3˚C
2. Deviation = 99˚C - 100˚C = -1˚C
3. Deviation = 101˚C - 100˚C = 1˚C
4. Deviation = 98˚C - 100˚C = -2˚C
5. Deviation = 100.5˚C - 100˚C = 0.5˚C
The observation with the smallest deviation from the accepted value is 100.5˚C. Therefore, 100.5˚C is the most accurate temperature for the boiling point of water among the given observations.
Suppose you work at a theme park. Your supervisor wants you to make a sign displaying the maximum weight that a roller coaster train can carry. Your supervisor knows that the maximum weight is 1686.5 kg. However, he wants the sign to be quickly understood and tells you to make a sign that says: Maximum Weight 1700 kg. How could the lack of precision in this example cause problems?
The lack of precision in this example could cause problems because it creates a potential safety hazard. By stating the maximum weight as 1700 kg, there is an inaccurate representation of the actual maximum weight of 1686.5 kg. This discrepancy of 13.5 kg may seem insignificant, but it can lead to potential issues.
Here are a few problems that could arise due to the lack of precision in the sign:
1. Overloading the roller coaster: If visitors see the sign stating a maximum weight of 1700 kg, they may mistakenly believe that it is safe to exceed the stated weight limit. This could lead to individuals or groups with a combined weight above 1700 kg boarding the roller coaster, which would place excess stress on the ride and potentially compromise its structural integrity. This could result in accidents or breakdowns during operation.
2. Mismatched expectations: Visitors who are aware of the precise maximum weight limit (1686.5 kg) may be confused or distrustful of the sign stating the rounded weight of 1700 kg. They may question the accuracy and reliability of other safety information throughout the park, which could lead to a diminished sense of safety and enjoyment for the guests.
3. Legal implications: In the case of an accident or injury involving the roller coaster, the lack of precision in the sign could be used against the theme park in legal proceedings. Lawyers could argue that the park intentionally provided inaccurate information by rounding up the maximum weight, potentially leading to negligence claims and legal consequences.
In summary, the lack of precision in this example can lead to confusion, safety hazards, and legal issues. It is essential to provide accurate and precise information, especially when it comes to safety guidelines, to ensure the well-being and satisfaction of park visitors.
Which of these measurements is expressed with the most significant figures?
Question 6 options:
0.20008 kilometers
150 liters
0.000342 grams
1.5 × 104 light years
The number of significant figures in a measurement is determined by the digits that are known with certainty plus one uncertain or estimated digit.
Let's count the number of significant figures in each measurement:
1. 0.20008 kilometers - There are six digits known with certainty, so there are six significant figures.
2. 150 liters - Since there are no decimal places and there are no trailing zeros, it is uncertain how many of the digits are significant. To make it clear, we can write it in scientific notation as 1.50 x 10² liters, which indicates that there are three significant figures.
3. 0.000342 grams - There are three digits known with certainty and two uncertain digits, so there are three significant figures.
4. 1.5 x 10^4 light years - In scientific notation, the decimal point indicates that all the digits are significant. Therefore, there are two significant figures.
Based on the analysis above, the measurement expressed with the most significant figures is 0.20008 kilometers, which has six significant figures.
If a can of soup contains 12.0 ounces (oz) of soup, how many grams of soup is that, in proper significant figures?
1 lb = 16 oz
1 lb = 454 g
Question 7 options:
624 g
340 g
340.20 g
0.423 g
To convert ounces to grams, we will use the conversion factor: 1 lb = 454 g.
Given that 1 lb is equal to 16 oz, we can set up a proportion to convert 12.0 oz to grams:
(12.0 oz) / (16 oz) = x g / (454 g)
Simplifying the proportion:
(12.0 / 16) = x / 454
0.75 = x / 454
To solve for x, we multiply both sides of the equation by 454:
x = 0.75 * 454
x = 340.5
Since the given value of 12.0 oz has three significant figures, the calculated value should also be expressed with three significant figures.
Therefore, the number of grams in 12.0 ounces of soup is 340 g, rounded to three significant figures. The correct option is 340 g.
What is the density (g/mL) of a sample of mineral oil if 250 mL has a mass of 0.23 kg?
Question 8 options:
57.5 g/ml
5.8 g/ml
0.92 g/ml
0.0092 g/ml