 In this video we’re going to go through
how to do metric conversion involving multiple prefixes like going from
nanosecond to kilosecond, megalitre going to picoliter, gigameter cubed you going to
hectometer cubed just to name a few. I’m going to share with you a foolproof
method and tips to make sure you’ll be able to do the conversion successfully.
I’ve talked about SI prefixes and an easy way to remember all twelve prefixes
in a video I’ve posted last week. Do watch it if you haven’t seen it. The link
is on the top right corner and in the description box below. I also went
through a foolproof method for converting between units in a video I’ve
posted recently. Do check it out if you need an intro on this method. We’ll be
using the same method in this video and we’ll expand on it since we’ll be
performing multi-step conversion. Let’s start with our first example. Question is asking us to convert from nanosecond to kilosecond. So since this involves two
prefixes, I’m gonna break it down where I will convert from nanosecond to second
and then second to kilosecond. That will involve two conversions. The reason why I’m not going from nano all the way to kilo is because I don’t know or I can’t
be bothered to memorize the relationship between nano to kilo.
Whereas I remember the prefixes, so I can always go back and forth between prefix
to the base. So even though it involves two steps, to me it’s a safer method.
So recall nano is ten to the power of negative nine so one nano second is 10
to the negative nine second and now we go from second to kilosecond. So one
kilosecond is 10 to the power of three second. Knowing these two prefixes is
what we’re gonna need to convert from nanosecond to kilosecond. So let’s start
with what we are given. 41 nano second multiply draw a line across so
we’re gonna place nanosecond at the bottom so we can cancel it off later and
now we’re gonna place the unit that we want the first type of conversion is
going to be from nanosecond to second that means
I’m gonna place my second on the top here that way my nanosecond will cancel
off so now I have second. Then we place in the value so the first relationship
is one for nanosecond 10 to the negative 9 per second so right now what we have
is the unit for second. So from second we are going to convert
it to kilosecond, so I’m just gonna do everything in one shot which makes life
easy. So multiply draw a line across so now take a guess what’s the unit we’re
gonna place at the bottom? Second, so that way second and second can cancel off and
the unit we’re gonna place on top is the unit that we want which is kilosecond.
So second cancel off each other and we’ll be left with kilosecond. Now the
next thing we need to do is place in the values. So in front of kilosecond it
should be one in front of second it should be ten to the power of three so
when we do the math we punch in the calculator 41 times 10 to the power of
negative 9 times 1 divided by 1 divided by 10 to the power of 3 that will give
us 4.1 times 10 to the negative 11 kilosecond. Iin fact you don’t have to
worry about multiply one divided by one because anything multiplied by one or
divided by one is anything whatever that values is. Let’s practice using another
example. Now we’re going to convert from 0.00832 to megalitre
to picoliter. So we’re going from megalitre to picoliter so the two
prefixes involve here is mega and pico. So we should go from megalitre
to liter and then liter to picoliter. That way we don’t have to crack our head
and try to find out the relationship between mega all the way to pico. We
can break it down going from mega going to the base unit and then from the base
unit going to pico, so mega is 10 to the power of 6. Pico is 10 to the power of
negative 12, so we’ll do the same way everything in one shot start off with a
value that’s given 0.0832 megalitre multiply draw a line
across. So we’re gonna place megalitre on the bottom and we’re gonna place
liter on the top because we are going to convert from megalitre to its base unit which is liter. Now the megalitre will cancel off each other. That will leave us with liter. Now
we’re gonna put in the value so we put one in front of megaliter and 10 to the
power of six in front of liter. Now we’re gonna do the second step of the
conversion which is from liter to picoliter, so multiply draw a line across and
then we’re gonna place liter at the bottom and picoliter on the top so that
way liter and liter can cancel off and we’ll end up with picoliter and then the
same thing put in the numbers one. In front of pL, ten to the negative twelve
in front of liter, and that will give us 8.32 times ten to the power of 17 picoliter. Now for our final example, let’s do something a little bit
more difficult. Let’s convert 6.3 Gigameter square to hectometer
square, so we’re going from Gm cubed to hm square. Again as what we’ve done let’s break it down to two parts, so we go from Giga to base unit, base unit to hecto.
From the prefix we know one Giga is 10 to the 9. 1 Hecto is 10 to the 2 so we
start off by 6.3 Gigameter square and then we multiply and we draw a line
across and so we’re gonna place Gigameter at the bottom and meter on the top.
From the first conversion we place one in front of Gigameter 10 to the 9 in
front of meter so far it’s the same as the last two examples. Before we proceed
we need to square everything so that Gigameter square can cancel off with
Kilometer square. So now we have meter sqaure square on the top so we go through the
same conversion multiply draw a line across and every place meter at the
bottom so that later we can cancel out the meter. Hectometer on the top because that’s the unit that we want but we’re not there yet. Let’s place in the numbers one for hectometer 10 to the power of 2. In front
of meter now we need to do the same thing which is square everything so
that middle square can cancel off with the square. To simplify everything so
it’s easier to read I’m going to retype it out 6.3 gigameter square times 10 to
the power of 18 meter square over 1 giga meter square times 1 hecta meter
square over 10 to the power of 4 meter square. So our gigameter square will cancel each other out and our metre square will
cancel each other out so after doing the math, 6.3 times ten to the 18
over 10 to the 4 that will give us 6.3 times ten to the 14 and the
unit is going to be hectometer square. In the first line of our calculation if you