Physics Question on significant figures?

In summary, the first problem asks for the length of a wire needed to form a circular arc with a radius of 8.1 cm and subtending an angle of 1.6 rad. The answer should be presented with two significant figures. The second problem asks for the average speed of Mizuki Noguchi, the winner of the Women's Olympic Marathon in 2004, in meters per second. The answer should be presented with four significant figures.
  • #1
Judas543
6
0

Homework Statement



1)
How long a piece of wire would you need to form a circular arc subtending an angle of 1.6 rad, if the radius of the arc is 8.1 cm?
Express your answer using two significant figures.

2)
In 2004 Mizuki Noguchi of Japan won the Women's Olympic Marathon, completing the 26 mi, 385 yd course in 2 h, 26 min, 20 s. What was Noguchi's average speed, in meters per second?

Express your answer using four significant figures.
 
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  • #2
Welcome to PF,

What are your thoughts so far? Can you show us your approach or your attempts? The other two parts of the homework help question template are equally important. What are the relevant relations or concepts that apply here (2), and what steps have you taken (3)?

By the way, neither of these problems is actually about significant figures. The first one tests your knowledge of the radian system of angular measure, and the second one has to do with the definition of average velocity.
 
  • #3
Is your problem about the number of significant figures? If it is, simply calculate the answer, and round off so that you present an answer with two digits.

86.725235 on your calculator becomes 87,

941.2 becomes 940

7.5912304 becomes 7.6, etc.
 

1. What are significant figures and why are they important in physics?

Significant figures are the digits in a number that have meaning and contribute to the precision of a measurement. They are important in physics because they help to communicate the accuracy and precision of a measurement. Using the correct number of significant figures is essential for making accurate calculations and drawing accurate conclusions.

2. How do I determine the number of significant figures in a measurement?

The general rule for determining the number of significant figures in a measurement is to count all non-zero digits and any zeros between non-zero digits. For example, in the number 0.00450, there are three significant figures. However, there are some specific rules for determining significant figures in more complex situations, such as with zeros at the end of a number or in a number with a decimal point. It is important to consult a reliable source for these rules.

3. Can significant figures be added or subtracted?

When adding or subtracting measurements, the result should have the same number of decimal places as the measurement with the fewest decimal places. This means that the significant figures may change in the final result. For example, if you add 2.3 and 4.56, the result should be reported as 6.9, with two significant figures.

4. What is the significance of rounding in significant figures?

Rounding is important when dealing with significant figures because it helps to maintain the correct number of significant figures in a calculation. When rounding, you should always round the last significant figure, and if the digit following it is 5 or more, round up. For example, if you have a number with four significant figures and need to round it to three significant figures, you would round to the nearest tenth.

5. Are significant figures only important in experimental measurements?

No, significant figures are important in all types of measurements, including experimental and theoretical. In theoretical calculations, the number of significant figures should be based on the least precise measurement used in the calculation. This ensures that the final result is not reported with more precision than is supported by the original data.

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