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I tried to follow along with this units video (https://youtu.be/hQpQ0hxVNTg) and convert 60 miles per hour to light years per second. I don't get the same answer as the video does. I feel really dumb!

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I just try to multiply through? and get: $$ \frac{60ly}{60*60*5.9*10^{12}sec} = \frac{1ly}{60*5.9*10^{12}sec} = \frac{1ly}{3.54*10^{14}sec} $$ or $3.54*10^{-14}$ light years per second

please halp!

lonious
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1 Answers1

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The video is wrong. I have no clue where they arrived at that number.

First - note that $\frac{1}{x} \neq x$ unless $x = \pm 1$. That is,

$$ \frac{1}{3.54 \cdot 10^{14}} \neq 3.54 \cdot 10^{-14}.$$

Instead, that is equal to $2.824 \cdot 10^{-15}$ which is the correct value you should arrive at. See this Wolfram query. I also verified this on my calculators.

Sean Roberson
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  • This answer looks very different than the video's approximation! The video number expands to 0.0000000000093ly/s while this one is 0.000000000000002824ly/s Also thank you for correcting the mistake I made while trying to move my scientific notation to the numerator. – lonious May 21 '23 at 00:28
  • I'm still a little bit confused on how $\frac{1}{3.5410^{14}}$ is somehow equivalent to $2.82410^{-15}$? Or are they not equivalent? Also doesn't the Wolfram query say 2.835 instead of 2.824? – lonious May 21 '23 at 00:48
  • Just punch it in your calculator and you'll see. – Sean Roberson May 21 '23 at 00:50
  • ah thanks again! I guess Wolfram might be using a slightly different constant for the light years to miles fraction? Just guessing. That might be the difference between Wolfram and us. – lonious May 21 '23 at 00:54
  • No - just more decimal digits used – Sean Roberson May 21 '23 at 00:57