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

had missed out the square your answer is going to be wrong. So please make sure

whenever you have questions involving like square or cube. When you put in the

conversion factor please make sure you remember to put in the square or the

cube. In this example its square, so you need to make sure that you put in the

square otherwise your answer is going to be wrong. We went through three examples together, so how about you try one on your own? Try converting 0.84 nanometer

to kilometer. I’ll place the answer in the description box below. Thanks for watching and I’ll see you in the next video.