How Do You Calculate Arc Length and Average Speed with Significant Figures?

AI Thread Summary
To calculate the arc length for a circular arc subtending an angle of 1.6 radians with a radius of 8.1 cm, use the formula L = rθ, resulting in an answer of approximately 13 cm when expressed with two significant figures. For Mizuki Noguchi's average speed during the marathon, convert the total distance of 26 miles and 385 yards into meters and divide by the total time in seconds, yielding an average speed of about 3.66 m/s when rounded to four significant figures. The discussion emphasizes that the problems focus more on understanding angular measures and average velocity rather than significant figures themselves. It suggests that once calculations are made, rounding to the appropriate significant figures is straightforward. Overall, the key takeaway is the importance of applying the correct formulas and concepts to arrive at accurate answers.
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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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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.
 
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.
 
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