Question

dimensional analysis question?
Convert 36.70 miles/hour into meters/second.
I have 984.379633333333333 repeating but how do i do sig figs or round the number?

Answer 1

In the first unit it has 4 significant digits!
So in metres/second also it'd have the same number of SF!
So write it like = 984.37963 = 984.3796 = 984.38 = 984.4 [4 significant figures]
Got it? :)

Answer 2

It depends upon how many digits you wish to maintain after the point. if you want to maintain two digits after the point do the following:
1) if the second number was greater than 5, round the number to the nearest biggest number after it whose second number is zero. for ex, 46 tends to 50.
2) if the second number was smaller than 5,round the number to the nearest smallest number after it whose second number is zero. for ex, 43 tends to 40.

Do it for multiple significant digits.

Answer 3

Hi! I want to make a couple points! @AkashdeepDeb is right about counting the significant figures of your that first number!

When you multiply or divide, you just make sure you have the same number of significant figures retricethe number with the least significant figures. And that's all you do when you convert!

Also, when you round, you go right to the digit you're rounding! Example:
\(.0845\rightarrow .08\)
If you do it in parts, you might have a problem. Example:
\(.0845\rightarrow .085\rightarrow .09\), but \(.0845\cancel\rightarrow .085\).

And I'm not sure if that calculation is correct..

Answer 4

You can convert miles to meters since they're both the same "dimension," distance.
Same with hours to seconds.
\(1\ [mile]=1609.34\ [meters]\)\(\implies 1=\dfrac{1609.34\ [meters]}{1\ [mile]}\)
\(1\ [hour]=3600\ [seconds]\)\(\implies 1=\dfrac{1\ [hour]}{3600\ [seconds]}\)

Now,\[36.70\ \left[\frac{\cancel{miles}}{\cancel{hour}}\right]\times\dfrac{1\ [\cancel{hour}]}{3600\ [seconds]}\times\dfrac{1609.34\ [meters]}{1\ [\cancel{mile}]}\]

You are not changing the actual value of velocity because you are multiplying it by one, twice.
\[=\frac{36.70\times 1609.34}{3600}\ \left[\frac{meters}{second}\right]\]

Answer 5

After calculation, make sure there are four significant figures!

Answer 6

984.8 is what I would use.

Answer 7

@jai2796 , how would you get that?