Why Are Units and Significant Figures Crucial in Scientific Calculations?

[XTEND]

Interpreting Results?

Homework Statement

A student recently submitted a homework solution in which he or she had calculated
an angular velocity w = 0.0002 rad/s (for a satellite going around the Earth.) The
student then found the period by using T = rad /w = 31415.92 seconds. Describe why
both answers are unacceptable. This is not about any formulae — it is about the
results that are given. (Your discussion should contain 4 or 5 sentences at the least.)

Homework Equations

N/A

The Attempt at a Solution

I think scentific notation should be applied, but other than that? Not sure what they want.

TIA

 

[rl.bhat]

When a satellite going around the Earth, the centripetal force is provided by the gravitational froce of Earth on the satellite.
Hence m*w^2*R = GMm/R^2. Where R is the radius of the Earth and M is the mass of the earth. Where close to the Earth GM = gR^2 where g s the acceleration due to gravity. Using these values calculate w. and verify the result with the given value.

 

[nlightner]

As a scientist, it is important to carefully analyze and interpret results to ensure accuracy and reliability. In this case, the student's answers are unacceptable because they lack proper units and significant figures. The angular velocity should be expressed as 2.0 x 10^-4 rad/s, and the period should be 3.14 x 10^4 seconds. Without units and significant figures, the values cannot be properly understood or compared to other results. Additionally, it is important to consider the precision of the measurements and the uncertainty associated with them in order to determine the reliability of the results. Therefore, in order to improve the accuracy and validity of the student's answers, it is necessary to include proper units, significant figures, and consider the precision and uncertainty of the measurements.