Master Converting Metric Units in Scientific Notation: Learn the Simple Method!

[Imparcticle]

Class started as usual on Tuesday, as my conceptual physics teacher started us on notes on scientific notation. I'm usually good with numbers and having had experience in scientific notation, it was no big deal--at first. Later into our notes, my teacher started doing conversions using sci.not. I still understood it, but not the class. I may have been the only one who got it, and if not one of few in that particular class. Unfortunately, my teacher came back the following day with a whole new method that was supposed to be "simple". It has confused me entirely. So, we have a quiz tomorrow and I don't understand the subject...not a good mix.

Okay, initially he did the problems for conversion by using conversion factors. For example, he would convert mm to nm and then convert to scinot. I totally understood that. BUT, he moved on to conversions involving things like: 10cm²= km². I figured out how you would do this kind of problem; just do the conversion as though there were no ^2s and after the conversion multiply the exponent by ^2. But apparently I was mistaken because my teacher started working out the problem in a way which I did not understand and eventually stopped and said he would go and figure out a simpler way.

The simpler way is indeed simple: you just use a chart with labled conversion units. So if you are converting m to dm, you count the place values from m to dm and use that for some sort of decimal operation. I don't quite get it.

Anyway, can someone please, please help me with converting metric units in scinot?

here are some conversion problems from my hmwk for example:

10.0 cm²= ___________m²

1.45 x 10[su]9[/sup] = ___________ Gm (I really need help with this one)


thanks

 

[robphy]

Here are some hints.
Since 1 cm=10^-2 m,
5 cm³= 5 (10^-2 m)³ = 5 (10^-2)³ m³ = 5 (10^-6) m³.

 

[Imparcticle]

10 cm²____________m²

1cm=10^-2m
1.00 * 10^-4

is that right?

if so, can you help me with the second problem I posted?

thanks

 

[recon]

If I am not mistaken, 1 cm² = 10^-4m²

So, 10 cm² = 10 x 10^-4m² = 10^-3m².

I don't think your second question was clear. Was it 1.45 x 10⁹cm or 1.45 x 10⁹m or something else?

 

[Imparcticle]

How do you get -3 as an exponent?

 

[Math Is Hard]

10¹ * 10^-4= 10^-3

or more generally

a^m * aⁿ= a^(m+n)