Physics - converting?

Question

I'm a little lost. I have that basic list of the prefixes for pico, nano, micro, milli, centi, kilo, mega, and giga. I just don't know how to apply it!

Convert 1cm into nanometers.

If you could, please explain step by step how to solve this (I have a full page of equations that I need to do so I should probably understand how to do it! haha) thank you :o)

Answer 1

Here's what I do

1. convert to scientific notation (you'll need to memorize what each prefix corresponds to)

They are:

pico = 10^-12

nano = 10^-9

micro= 10^6

milli = 10^-3

centi = 10^-2

kilo = 10^3

mega = 10^6

giga = 10^9

so knowing that you find the difference in exponents

for this 10^-2 (cm) and 10^-9 (nano) the differnt is -2 --9 = 7 since it's positive we move our decimal point to the RIGHT 7 spaces making 1 cm 10,000,000 nanometers  If the number came out negative we'd move to the left.

Answer 2

I do it with fractions

1 cm * ( 1 m /100 cm) * (1,000,000,000 nm / 1m)

1m/100cm is just another way of writing 1 because top and bottom are the same thing

same for (1,000,000,000 nm / 1m)

Now I cancel units

1*1/100*(1,000,000,000) nm = 10,000,000 nm

Answer 3

Make it a practice of using dimensional analysis for solving problems. You will find it a very useful tool for determining units, and checking the result of an equation.

Use your list to find each prefix and the corresponding power of 10.

1 cm * 10 mm/1 cm * 1000 um/mm * 1000 nm/um = 10e7 nm

Notice how a length unit in the denominator of each conversion factor cancels a unit in the numerator until what is left is the unit you want.

What you are effectively doing is multiplying by 1 in each step, so you are not changing the value, just the length unit. This works for all equations.

Here's a handy link about dimensional analysis with a lot of examples:

http://alysion.org/dimensional/fun.htm

Here's a link to an on-line conversion site:

http://www.onlineconversion.com/

Answer 4

1cm = 1 x 10^-2 m

1nm = 1 x 10^-9 m

The longer, easier way is convert from cm to meters, then meters to nm.  Use the conversion table to divide by the current units and multiply by the units converting to:

1cm = 1 x 10^-2 m (by definition, no need to convert)

1 x 10^-2 m = (1 x 10^-2 m)x (1nm/1 x 10^-9 m) = 1 x 10^7nm

This method will work with any conversions, but the metic system is nice because you can convert just by subtracting the exponent of the unit are going to from exponent of the unit you started with:

1cm = 1 x 10^-2 m <--- exponent -2

1nm = 1 x 10^-9 m <--- exponent -9

(-2) - (-9) = 7

So, you can convert cm to nm by multilying by 10^7.  

Doing the same for nm to km would be (-9)- (3) = -12 giving 1 x 10^-12 km = 1 nm.

Answer 5

To go from a basic unit say meter to another, move the decimal point the number of places that the new unit is raised to the power of ten of. Huh?

here is an example:

deci- d 10^-2

centi- c 10^-2

a centimeter is a meter times 10^-2

so if you are given a meter and need to convert it to centimeters you move the decimal point two places to the right. (12.00 m = 1200 cm)

But:

kilo- k 10^3

To convert meters to kilometers move the decimal place 3 places to the left. (1,345.0 m = 1.345 km)

to go from centi to kilo, for example, simply subtract the exponents 3 - (-2) = 5  which means move 5 places to the left ( 12345321.0 cm = 123.453210 km)

It's really easy if you have a simple chart with all the prefixes and powers of ten.

Here's one:

http://www.essex1.com/people/speer/large...

1.000000 cm = 10000000.0 nm

Have fun!