Rounding to the correct decimal place

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aron silvester
1. The problem statement, all variables, and given/known data
This is an experiment of dropping the ball 5 times at eye level, and we record the seconds that it takes the ball to hit the ground in seconds. The second's measurement has two digits after the decimal. Should the Average and Standard Deviation be rounded to the nearest hundredths place as well?


Homework Equations


Two equations: standard deviation sigma_x equals the square root of the sum from i=1 to N of (x_i minus x_avg) squared, divided by N minus 1; and the average x_avg equals one over N times the sum from i=1 to N of x_i.

The Attempt at a Solution

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Table 1 of ball drop timing: five measurements of time to hit the floor in seconds, 0.57, 0.49, 0.41, 0.36, 0.46, with average 0.458 and standard deviation 0.0798, handwritten in red.
 
aron silvester said:
1. The problem statement, all variables, and given/known data
This is an experiment of dropping the ball 5 times at eye level, and we record the seconds that it takes the ball to hit the ground in seconds. The second's measurement has two digits after the decimal. Should the Average and Standard Deviation be rounded to the nearest hundredths place as well?
Both should be rounded to two significant digits, which isn't necessarily the same as rounding to the nearest hundredths. For your computed average these will be the same, but for your std. dev., you should round to the nearest thousandth. I.e., .0798 will round to .080, with the 8 digit and the last 0 digit being significant digits.
aron silvester said:


Homework Equations


View attachment 210860

The Attempt at a Solution

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View attachment 210859
 
aron silvester said:
1. The problem statement, all variables, and given/known data
This is an experiment of dropping the ball 5 times at eye level, and we record the seconds that it takes the ball to hit the ground in seconds. The second's measurement has two digits after the decimal. Should the Average and Standard Deviation be rounded to the nearest hundredths place as well?


Homework Equations


View attachment 210860

The Attempt at a Solution

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View attachment 210859

Your standard deviation is ##0.798 \times 10^{-1}##, which rounds appropriately to to ##0.80 \times 10^{-1} = 0.080##. The answer has two significant figures but three decimal places when written in fixed format instead of scientific format.