Converting units in scientific notation to other units.

[CinderTwig]

I'm having some trouble with a few problems that I'd really appreciate some help with.

1.) The velocity of a space shuttle is 8 x 10^3 meters/seconds

I have to convert this to kilometers/hours. I know there are 1000 meters in a kilometer, and 3600 seconds in an hour.

Next I have to convert meters/seconds to miles per hour!

However, I don't know how to put these into an equation to solve. :( The same goes for the following problem:

2.) 3 x 10^-1 joules/minutes

How many watts is this?

I know 1 watt = 1 joule/seconds, but again don't know how to put it into an equation.

The next part is how many miliwatts is produced?

I am just looking for how to put these into a solvable equation--I can take it from there. :)

Help would be greatly appreciated!

 

[mgb_phys]

It's just a matter of being careful about which way up you have the conversions

8x10^3 m/s = 8000 m/s
There are 1000m in a km = 1000m/km, we want an answer with km on the top - so we need to do

8000 m/s / 1000 m/km = 8 km/s (remember something divided on the bottom goes on the top - just like fractions.
Then there are 1.6km in a mile so divide by 1.6km/mi = 8km/s / 1.6km/mi = 5km/s

 

[Mentallic]

If you have x .\frac{m}{s} then if you want to change anything you need to keep the fraction balanced, as in if the numerator is changed, the denominator needs to be changed in the same way, for e.g. converting to km/s (1km=1000m):

\frac{x}{1000}. \frac{1000m}{s}

\frac{x}{1000}. \frac{km}{s}

Now convert to km/h with 1h=3600s:

\frac{3600x}{1000}. \frac{km}{3600s}

\frac{3600x}{1000}. \frac{km}{h}

Now just simplify and you have 3.6x. \frac{km}{h}

This is basically saying that x m/s = 3.6x km/h

Try this for the rest

 

[Bohrok]

Or use conversion factors/labels

\frac{8\times 10^3 ~meters}{1 ~second}\left(\frac{1 ~kilometer}{10^3 ~meters}\right)\left(\frac{3600 ~seconds}{1 ~hour}\right)

It's easy to keep track of what units cancels and what you have left to multiply or divide.

 

[Mark44]

The best explanation I've heard makes use of equations that convert from one unit to another. In your first problem you need to convert meters to miles, and seconds to hours.

The two equations we need are
1 mile = 1609.344 m.
1 hr = 3600 sec

In the first equation we can divide both sides of the equation by "1 mile" to get
1 = 1609.344 m/mi.

Alternatively, we can divide by "1609.344 meters" to get
\frac{1 mi}{1609.344 m} = 1

In the second equation we can proceed similarly to get
1 = 3600 sec/hr or
\frac{1 hr}{3600 sec} = 1

Since these expressions are all equal to 1, we can multiply anything by them without changing its value.

Your original expression is 8 * 10³ m/sec. Since we need to convert m/sec to mi/hr, we need to cancel m and sec and end up in units of mi/hr.

To cancel the m (meters) I need the conversion that involves mi/m. To cancel the sec, I need the conversion that involves sec/hr.

8 * 10^3 \frac{m}{sec} * \frac{1 mi}{1609.344 m} * \frac{3600 sec}{1 hr}
= 8 * 10^3 * \frac{1}{1609.344} * \frac{3600}{1} * \frac{m}{sec} * \frac{mi}{m} * \frac{sec}{hr}

As you can see, the m units cancel, and the sec units cancel, and we're left with units of mi/hr. The numbers multiply to 17.89549034 * 10³ mi/hr, or 1.789549034 * 10⁴ mi/hr = 17895.49034 mi/hr.

 

[CinderTwig]

Ahh, thank you all very much for the help! :) I was able to solve the problems alright.