This is how to use the number-line method,
I like to call it the "reverse number-line method"
to convert units with one prefix to
another prefix in the metric system.
This method will work for any units that have prefixes
in front but it will not work for cubic units
like cubic centimeters or cubic meters. So
let's try what we do first is we use a
reverse number line and a reverse number line has
powers of ten in it. So we start with
ten to the power of 6 on the left side and then
each line here represents a power of ten.
Now ten to the fifth and ten to the fourth
don't have prefixes; ten to the third does:
ten to the third is kilo, ten to the sixth
is mega. We put ten to the zero for the base unit,
and then ten to the -2 is centi-, ten
to the -3 for milli-, this is micro,
this is nano-, and this is pico. And we'll use
this reverse number-line method to convert
from one unit to another. So let's try a problem
here: Converting 25 cm to nanometers.
To do this, place the decimal point of the number
with the appropriate prefix: in this case,
centi. So you put the decimal point here for
ten to the -2. Now if the number had been
25 meters, without any prefix at all, then
we put it at ten to the 0, but here we put
it ten to the -2 for centi-. And then you
put the numbers in. You put the numbers
so that the numbers are between the lines. Like
this. Notice that it's 25. Now if it had been
2.5, then I would place the 2 here and the
5 here if it had been 2.5, but it's 25 here.
And then, to convert to nanometers, simply
move the decimal point over to where the nano- is.
And then you notice that I have to fill
in the zeroes here between each line. So
25 and 7 zeroes afterwards to go from centimeters
to nanometers. Let's try another one: 254.2
nm to cm, so this time we're going from a
smaller unit to a larger unit. Put the number in,
but before you put the number in put the
decimal point in. It's by the nano- this time.
And then put the number in: remember to put
the number in between the lines. 254.2.
and now we convert to centimeters by moving the
decimal point to centi- -- keep the numbers
of course where they are--fill in the zeroes
and there's your answer.
