Math Is Fun Forum

Cinder

Guest

Problems Using Scientific Notation and Converting Them Into Units.

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 problems:

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?

Help would be muchly appreciated!

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Problems Using Scientific Notation and Converting Them Into Units.

#1.)
8 x 10^3 meters / second = VeSpSh = Velocity Space Shuttle
1 meter = 1 kilometer / kilo = 1 kilometer / 1000
1 second = 1 hour / 3600
Reciprocals are useful too: 1 / second = 3600 / hour
Another reciprocal might help: 1 / meter = 1000 / kilometer
I just flipped over the fractions above for reciprocals.

Replace meters with 1 kilometer / 1000.
Replace 1/second with 3600 / hour.

VeSpSh * (kilometer / 1000) * (3600/hour)
10^3 / 1000 is 1.
8 kilometer * 3600 / hour
28800 kilometer / hour
288 x 10^2 (same units)
2.88 x 10^4 kilometer / hour
That should be the answer.

There are two basic ideas for unit conversions.
Either "replace" units with other units like I have done, or
use multiplication "conversion factors" which is probably
the same thing, but more confusing.   With conversion
factors, the top and bottom of fractions are the same
units like "inches" and they cancel out leaving you with
new units.  But I did a simple replacement, like
1 / second, I replaced with 3600 / hour.
Knowing how to do reciprocals is important.

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igloo myrtilles fourmis

Cinder

Guest

Re: Problems Using Scientific Notation and Converting Them Into Units.

Thank you very much for the help!