General Physics I: Units and Measurements

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Questions and Answers

What is the definition of accuracy in measurements?

The level of variation in repeated measurements

The consistency of measurement results over time

The closeness of measurements to each other

The closeness of measurements to the actual value (correct)

Which of the following examples best illustrates precision?

Measuring the weight of an object three times and getting 5.1 kg, 5.1 kg, and 5.2 kg. (correct)

Measuring the temperature of water and getting 25°C, 30°C, and 25°C.

Measuring the length of an object with values of 2.0 cm, 3.0 cm, and 2.5 cm.

Measuring the height of a building and consistently getting values around 100 m.

What determines the precision of a set of measurements?

How close the measurements are to the true value

The standard value against which measurements are compared

The spread of the measured values in the set (correct)

The method of measurement used

Which statement is true regarding accuracy and precision?

Accuracy can occur without precision. Signup and view all the answers

If three measurements of a standard length are 10.0 in., 10.1 in., and 10.1 in., what can be concluded about their accuracy?

The measurements are accurate if the true length is 10.0 in. Signup and view all the answers

How does one assess the precision of a measurement series?

By determining the range between the highest and lowest measurements. Signup and view all the answers

What is a potential outcome of measurements being precise but not accurate?

The measurements are consistently off from the true value. Signup and view all the answers

In the printer paper measurement example, what did the range of the measurements indicate?

The measurements had low variability. Signup and view all the answers

Which statement about significant figures is correct?

Any digit that is not zero is significant. Signup and view all the answers

How many significant figures are in the measurement 0.0045 m?

2 Signup and view all the answers

In the number 2020.0, how many significant figures are present?

5 Signup and view all the answers

When rounding off the number 6.567 to three significant figures, what is the result?

6.57 Signup and view all the answers

How would you express 0.07080 km in terms of significant figures?

4 significant figures Signup and view all the answers

What is the proper significant figure representation of the measurement 543.0 L?

4 significant figures Signup and view all the answers

Which of the following numbers has the greatest number of significant figures?

60.0508 kg Signup and view all the answers

If a number is rounded and the digit to be dropped is less than 5, what happens?

The last digit remains unchanged. Signup and view all the answers

What is the correct standard notation for the scientific notation $6.98 \times 10^9$?

6980000000 Signup and view all the answers

How many places would the decimal point move to convert $0.00698$ into scientific notation?

3 places to the left Signup and view all the answers

What does a negative exponent indicate when converting from scientific notation to standard notation?

Both A and C are correct Signup and view all the answers

What is the standard notation for the scientific notation $9.30 \times 10^6$?

9300000 Signup and view all the answers

When converting the number $8 \times 10^{-2}$ to standard notation, what is the resulting value?

0.08 Signup and view all the answers

What is the result of rounding 235 g to two significant figures?

240 g Signup and view all the answers

When rounding 785 cm to one significant figure, what is the result?

800 cm Signup and view all the answers

How should the number 4,123 kg be rounded off to three significant figures?

4,120 kg Signup and view all the answers

What is the outcome when rounding 705 Ohms to one significant figure?

700 Ohms Signup and view all the answers

What is the correct representation of 0.37754 A rounded to three significant figures?

0.378 A Signup and view all the answers

If the digit to be dropped is a 5 and the retained digit is odd, what action should be taken?

Add 1 to the odd digit Signup and view all the answers

What is the scientific notation of 1.66054 x 10^-24 kg?

0.00000000000000000000000166054 kg Signup and view all the answers

How is the exponent determined when converting from standard notation to scientific notation?

By moving the decimal point left or right Signup and view all the answers

Study Notes

Accuracy and Precision

Accuracy measures how close a measurement is to the true or accepted value, e.g., measuring printer paper length close to 11.0 inches.
Precision assesses the closeness of repeated measurements to each other, indicating the consistency of results under identical conditions.
The range of values is a method for evaluating precision, calculated as the difference between the highest and lowest measured values; lower range indicates higher precision.
Possible scenarios: Measurements can be accurate but not precise, precise but not accurate, or both accurate and precise.

Significant Figures

Significant figures indicate the precision of a measurement device; more significant figures imply greater accuracy.
Key rules for identifying significant figures:
- Non-zero digits are always significant.
- Leading zeros do not count as significant.
- Zeros between significant digits are significant.
- Trailing zeros count as significant only if there is a decimal point.
Rounding off rules:
- If the digit dropped is greater than 5, increase the last retained digit by one.
- If the digit is less than 5, simply drop it; no increase needed.
- For a dropped digit equal to 5, round to the nearest even number.

Scientific Notation

Utilized for dealing with very large or very small numbers to streamline calculations.
Form consists of a digit term (1-9) and an exponential term (power of ten).
Scientific notation conversion:
- Copy significant digits, moving the decimal point to the right for large numbers and left for small numbers.
- Count movements and assign positive or negative signs to the exponent based on direction.
Conversion examples:
- Standard Notation (6,980,000,000) converts to Scientific Notation (6.98 x 10^9).
- Small numbers, like 0.00698, convert to (6.98 x 10^-3).

From Standard to Scientific Notation

Move the decimal point right for positive exponents and left for negative exponents to convert between notations.
Understanding movement direction is crucial for determining the sign of the exponent.

From Scientific to Standard Notation

Revert the process: move the decimal according to the exponent’s positive or negative sign.
Accurate movement results in correct representation in standard form.

This structured approach aids in mastering the foundational concepts of accuracy, precision, significant figures, and scientific notation in physics and measurements.

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Description

This quiz covers the fundamental concepts of units and measurements as discussed in Lesson 1.2 of General Physics I. Understand the differences between accuracy and precision, and how measurements relate to true values through practical examples. Test your knowledge about standard measurements and their significance in physics.