Rounding to the correct decimal place

[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

The Attempt at a Solution

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[Mark44]

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.

Homework Equations

View attachment 210860

The Attempt at a Solution

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View attachment 210859

 

[Ray Vickson]

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.