Mastering Unit Conversions for the Digital SAT Math Exam

hi everyone welcome to my Channel today test prep today we'll be going over orochento number two unit conversions

the goal of the otochento course is to teach students everything they need to know about the digital sat math exam

please see the link in the description to download this video's worksheet for free

let's get started okay so first thing we need to know are some must-know unit conversions

so some of these are going to seem kind of silly but I feel the need to go over it just for the sake of clarity so so

there's 60 seconds in one minute 60 Minutes in one hour and then this last one might not be

quite as obvious 60 times 60 is 3600 so there are 3 600 seconds in one hour and you are expected

to know all three of these going into the digital SAT Math tests now pretty much everything else they're

going to give you so you don't need to worry about the very common misconception I think this is a thing on

some other tests where you need to know like some common American units inches and feet and stuff like that so many

International students take the SAT that they know better than to not do that so they will pretty much give you every

single every single unit conversion you need to know so just the three that I have on screen are the ones that are

most important all right skill number one units from words

so the concept here is pretty much whenever you see the words each and per um either of those words usually

indicate that there's division going on in a unit so for example very common thing we say in America is 60 miles per

hour it's like the speed limit on a highway so miles per hour the units are actually

we would write that when we're doing math we would write it as miles divided by hour

let's do a quick example at the Whiteboard okay so for this guy

it says we want to find the rate in revolutions per

minute so we're going to do revolutions divided by

minute so they tell us 500 revolutions so that's going to go on the top

and 40 minutes and let's see what that gives us 500 divided by 40 is 12.5 so we would write

this as 12.5 revolutions per minute

and that is our answer okay let's move on to the next skill okay the second skill is we're going to

do one step unit conversions using the factor label method so here's a problem squirrel has a

length of 10 inches what is the scroll's length in centimeters and just like always on the SAT they give us the

necessary unit conversion and what we're going to do is we're going to first write down the thing

they're asking us to convert which is the 10 inches and then we're going to put a

parenthesis with either one inch on the top or bottom and then 2.54 centimeters on the top or bottom of the fraction so

you pretty much have a 50 50 chance of getting this right so what you do is

um hopefully once you practice you start to see kind of what goes where just by intuition but

what you do is you set it up and then you treat the division sign kind of like a fence

and if the units are on the opposite side the same unit is on opposite sides of the fence

then they cancel so you see here I did a good job inch and inch are on opposite sides so they're going to cancel if you

had it the other way if you had one inch on top and 2.54 centimeters on the bottom inches would be on the same side

so it would not cancel so you wouldn't be able to convert the unit so just before you move on always check to make

sure that the unit that you want to cancel is on opposite sides of the division sign

and you physically cross it out with your pencil so that you can see what units you are left with

so we're left with centimeters which is what we want so we're all good so all we got to do is now go into Desmos or our

calculator and type in 10 times 2.54 over 1 and that'll give us our answer which for this guy is

25.4 centimeters okay let's do another example at the Whiteboard

okay so this one says a hiking trail a success of 160 yards okay so that's what we're starting with so we're going to

write that down first and now I'm going to make a parenthesis and I'm going to put

1760 yards we're going to use the the unit conversion with yards in it which is this one

so we're using this guy and it does have yards in it so that unicorn version is good we don't need to

do anything to it and then I'm going to put the other part of the interim version on the bottom but

looks like I made a mistake here because um when I go to cancel I see the units of

yards are on the same side so it's not going to cross out so all I'm going to do is

I'm going to realize that I made that mistake and I'm going to switch these guys

like I said pretty much a 50 50 chance of doing it correctly every time you go to do a step of a you know conversion so

one mile goes on the top 1760 yards goes on the bottom and as you can see yards is on opposite

sides of the division sign so we can cross this out and we should be left with Miles and we

are so now all we got to do is is go into a calculator and put all these numbers in and I would

type it just exactly as written don't do anything in your head because that increases the chance of making a mistake

so I'm going to do 6160 parentheses 1 over 1760 and I get 3.5 so the answer for this guy

would be 3.5 miles and of course

you could change that to a fraction and put seven halves

but 3.5 works pretty good for our purposes here all right that's how you do a one step

unit conversion using the factor label method let's move on to the next skill okay skill number three is a multi-step

unit conversion using the factor label method so we have this problem corn plant has a

height of 96 inches what is the corn plant's height in yards and they tell us there's 12 inches in a

foot and three feet in a yard so we're basically going to do the same thing we did last time we're just going to do it

for a multi-step we're going to do it two or three times usually you don't see unit conversion more than two steps on

the SAT maybe once in a very blue moon there's a three stepper but for the most part there are one or two steps

so we're going to first write down what we're given which is the 96 inches and now I'm going to go okay which unit

conversion has inches in it well only one of them does the 12 inches in a foot so we're going to make a parenthesis and

we're going to either put 12 inches and one foot on the top or bottom accordingly

we're going to put inches on the bottom so that it cancels out with the 96 inches given in the problem so the units

of inches are both on opposite sides of inside so it cancels so we can cross it out with

our pencil and now if we were to stop right now and type this on our calculator we would

have the length in feet but that would just take a lot of time so it's far better if you just kind of continue

writing the rest of the conversion as I'm about to do here so we've got feet so we want a conversion factor with

feet in it well the three feet equals one yard that has feet in it so we're going to use that one and we're going to

accordingly put one on the top and one on the bottom so that the unit that we want to cancel cancels and I put feet on

the bottom so that it cancels out with the foot it's just singular feet on the top

and those are the same units so they do cancel and we can cross it out with our pencil and we're left with yard so now

if we go to our calculator and type in 96 parentheses 1 over 12 parentheses one over three

we should get our answer and we get 2.666 yards

you also could put the equivalent improper fraction that would be acceptable as well kind of depends you

know if they don't say anything about rounding just go with the improper fraction if they do mention like round

to the tenth round to the hundredth or it comes out nicely you can just use the decimal

okay let's do another example at the Whiteboard okay so for this one

we are told that we have 90 sarplar so that's what we're going to start with and we now want to use a unit conversion

with sarplar in it which is this one one sharp blur equals 80 tots so I'm going to come over here

and I want sarpler to cancel so I'm going to put one sharpler on the bottom and 80 Todds on the top

and let me check are they on opposite sides of the division sign they are

so the sharpler can get crossed out and we're left with Todd so now we want to use a unit conversion with Todds in

it so I see that's this one here and we're going to make another parentheses

and once again I'm going to put three ties I'm gonna put Todds on the

bottom hoping that I can get it to cancel 84 pounds on the top

and we do have Todds on opposite sides the division sign they're the same unit so they cancel out

and now we're left with pounds so we we want to use a unit conversion with pounds in it

which is this one so now we're going to come over here and I'm going to put

two two four zero pounds and 160 Stone on the top and pounds and let's just

again draw that little fence just to make this kind of even clearer and

pounds is on opposite side division side so we can cross that out so we're left with stone and if we go

and type 90 and all this big mess in our calculator um we should get our answer so please

please please make sure you know how to do that I'm going to do it on the screen now

um you'd hate to do all this work and then not get it right because you don't know how to type it in the calculator

right that would that would be terrible so um we're going to do 90 parentheses 80 divided by one Desmos makes this nice

and easy 84 divided by three and I'm just going to type it exactly as

written I don't want to there's no reason for me to increase the chance of making a careless mistake by doing some

of this fraction math in my head it's also going to slow me down if I do that okay 160 over 240. okay so I type it in

just like that and we should get 14 000

400. so let's jot that down let me just double check 90 times 80 over 1 times 84

over 3 160 over 2 240. good okay so we should get fourteen thousand four hundred

Stone as our answer okay that's how you do a multi-step unit

conversion let's move on to the next skill okay so skill number four

is rate unit conversions so let's look at this problem a pool is being filled at a rate of 120 gallons

per hour what rate is the pool being filled at in milliliters per second round to the

nearest tenth so they give us the conversion for gallons and milliliters but they don't give us the conversion

for seconds and hours so remember that's something you need to know so I'm gonna as soon as I would start this problem I

would write that down next to my work 3 600 seconds is equal to one hour we talked about that at the beginning of

the video so see they gave me the one about the volume but they didn't give me

the one about the time so you got to remember to recall that and write it down when you go to start a question

like this just like we did all right so we're going to write down 120 gallons per hour

um if you want just to make it easier to see some kids like to put a a one on the bottom just to make it more visibly look

like a fraction and I did that here I probably won't do it later in the video but don't pay much attention to that you

don't need that one on the bottom if you don't want it you could just put 120 and then gallons over an hour

and now we're going to um it doesn't matter which you tackle first I'm going to choose to tackle the

gallons first so okay so I'm going to make a parentheses um I'm going to put gallons on the

bottom and then milliliters on the top so that they cancel and we see gallons and gallons they're both on opposite

side of the division side so we can cross them out and now we're going to make another

parentheses and this is really weird and awkward and tough to get used to but as long as you practice you should be

okay the we're going to put like um uh another parentheses with the 3600 seconds one hour and this is a little

weird you might be kind of inclined to put the one hour on the bottom but you you'd find that that wouldn't

work we're canceling something not from the top but from the bottom like it's different than what we were doing before

so the one hour has to go on the top and the 3600 seconds has to go on the bottom many many people would have put the one

hour on the bottom forget to cross it out and they would have gotten a trap answer

um so please please before you move on just double check that one of the units you want to cancel is on opposite sides

of the division sign so hour is on both sides of the division sign so we can cross it out

and you see we're left with milliliters over seconds or milliliters per second which is what we wanted so now if we go

and type this big mess in we should get uh in our calculator we should get the answer

which rounded to the nearest tenth is 126.2 milliliters per second so very similar to what we were just doing it's

just that kind of extra step where you have to like cancel something out like kind of across the

aisle that can be kind of confusing so just just do some practice make sure you get used to that all right let's do one

more problem at the board okay so for this problem uh we got a plane is traveling at a speed of 660

feet per second what is the speed of the plane in miles per hour and they tell us 528 feet in one mile and I see we're

gonna have to change seconds to hours so we should first before we do anything write down the other unit conversion we

need which is 3600 seconds

equals one hour that's just something we should know okay so we're gonna we're gonna first

write down what we're given so 660 feet per second

and it doesn't matter which we tackle first why don't I do the feet first so

I'm going to put 5280 feet on the bottom and one mile on the top

we're using this one because that one is the one that has feet in it and they are on opposite sides of the

division sign so the feet it's the same unit on both sides so it cancels out and now we have miles per second

but we don't want miles per second we want miles per hour so we're going to make another unit

conversion and I can kind of again if I want you know just cross that out I'm not using

that one anymore um okay so we're gonna put 3 600 seconds on the top

and one hour on the bottom very strange it's kind of like the opposite of what we're doing before but again

um just make sure always that they're on opposite sides of the fence

so seconds is on opposite sides of the fence so we can cross that out and cross that out and

now we're left with miles per hour which is what we wanted so if we go and type this big mess in

we should get our answer so let's try that so 661 over 52 80

3600 over one and we get 450 so our answer is 450

miles per hour very similar to what we're doing before again just that you got to remember your

time conversions and it's a little strange like I said canceling out something kind of like

across the row here little strange take some getting used to but pretty much the same idea

all right let's move on to the next skill okay so skill number five is square unit

conversions and I promise you I promise you these are not so bad everyone gets them wrong

I promise you they're not so bad you just need to pay attention and you need to see an example so you know what

to do so let's look at this problem we have a

carpet with an area of five square feet what is the area of the carpet in square inches

so many people would just straight away try to do what we did before but

you see these units square feet and foot they don't cancel because they're not the

same thing one of them is a unit of length and one of them is a unit of area they need to look exactly the same

minus this whole singular plural English thing we do with feet they need to look pretty much exactly

the same first to be able to cross them out so many people would have said 60 for this one and that would be wrong so

what we just did on screen this just a common mistake this is not right do not ever do this

so there's something you got to do first which is you have to um change the unit conversion into

square units so they told us 12 inches is equal to one foot so what you're going to do is to get

square inches and square feet is you're going to square both sides of the equation which is a valid algebra

operation so unit of Opera rules of exponents now tells us that we can distribute that

power of 2 to both the unit and the number so we're going to write 12 squared inches squared equals 1 squared

foot squared 12 squared inches squared 1 squared is just one so you can call that one foot

squared and if you want you can change the 12 squared to 144 if that's easier for you

so really either of those at the bottom are fine to use um

I don't know I personally like to use the 144 but like when they give me like a problem with like a decimal I I'll

usually just write like 0.7 squared into my calculator just because that's easier I don't know for the sake of consistency

I'm going to use this top one just just do whatever works for you if you want to quickly type the decimal in and square

it on your calculator before you move on that's fine um just just just pick away and stick to

it so we now know that there's 12 squared inches squared in a foot squared

now after we do that we do the factor label method just like before so 12 square inches squared equals one

foot squared they told us five square feet or five feet squared and we're going to put one foot squared

on the bottom 12 squared inches squared on the top um the foot square and feet squared now

that they're the same unit they they and they're on opposite sides of division sign they cancel

and we put that in our calculator 5 times 12 squared over one and we should get 720 inches squared or

720 square inches let's do another example at the board oh almost forgot everyone before we do

the example um I have this slide here that just Recaps

um this might be kind of confusing if you're an international student because you might refer to like area and volume

units differently and um so I just wanted to make sure we're clear on this so if you see like Square in front of a

unit that means the unit is to the power of two so in this example square inches

means inches squared if you see on the SAT for example cubic centimeters

that would be centimeters cubed or to the power of three so see how Square tells us the units to

the power of two and cubic tells us the unit is to the power of three so just make sure that

um you understand that going into the test because the way they write it using

words might not be the most intuitive if you're more of a numbers person all right let's do the example now

okay so for this one they tell us we've got 2.3 square miles which I'm going to just write as

miles squared and we don't have a unit conversion with square miles we just have miles so we're

going to do what we talked about before we're going to square um both sides of the unit conversion

and we get 1 squared which is just one kilometer squared equals

0.62 squared miles squared and now that's going to be our

unit conversion so now we do the factor label method and we're going to put

zero point 6 2 squared miles squared and then one kilometer squared

and now that they're the same on opposite sides of the division sign we can cross out miles squared

and we're left with kilometers squared so now we just have to put or square kilometers as the question freezes it

so now we just need to type in 2.3 times 1 over blah blah blah let's do that so 2.3

parentheses 1 over 0.62 squared and we get that if you wanted to again

quickly just type in 0.62 squared and then just put that in instead of 0.60 squared that is fine just do what works

for you like I said with decimals it doesn't really make the problem any easier for

me so this one says to round to the nearest hundredth so we're going to say 5.98

uh square kilometers or if you want to just write that as kilometers squared all right awesome job let's go back to

the slides okay everybody we're going to get ready to do the final review now

so please make sure you remember to download the free final review worksheet using the link in the description

try to complete the worksheet yourself before watching the rest of the video and remember to be on the lookout for a

pinned comment on this video with more helpful links about today's topic let's go back to the Whiteboard and

finish the final review okay this first one um not really much going on here it just

kind of wants us to use our knowledge of units to figure out what to do so it says square feet of

grass per minute

so we're going to do square feet remember per

means divide per minute

so we're going to put the 450 square feet on the top you could write it as feed squared if

you want over 20 minutes and let's see what that gives us so 450

over 20 that's 22.5 square feet per minute

which is our answer all right very good okay now we're getting into the factor

label method which is the bulk of what we did today so um we've got eight thousand forty six

point seven meters and um I'm gonna put

The Meters from the unit conversion on the bottom here and I'm going to put the one mile on the

top and now I just check okay are they on opposite sides the division

sign meters they are it's the same unit on the opposite side so I can cross it out

and I'm left with Miles which is what we want so that is good so now I just need to put that into a

calculator so let's do that

so 8046.7 1 over 1609.34

[Music] and I get five so this guy is five

miles which is our answer okay question three so it says a phone has a mass of 0.175 kilograms

and we only have one unit conversion so I don't really need to

think too much about it but just check okay it's got kilograms in it so we can use it

and I'm going to put one kilogram on the bottom and a thousand grams

on the top okay do I have something on opposite sides division sign that cancel yep kilograms are the same on both sides

so those go away and we're left with grams which is what we want so we can now kind of forget

about all this and go to the calculator and again uh

0.175 times a thousand over one gonna put it in even though it might seem a little silly for this one gonna put it

in exactly as written just so I don't make a careless mistake and I get 175

grams which is our answer all right this one gave us

two so we have to do a multi-step unit conversion

so 120 yards do I have a unit conversion with yards in it yes I do this one so I'm gonna put one yard on the bottom

and three feet on the top and do the units cancel yes they do and I also don't need this guy anymore so

why don't I just cross them out and do we have a unit conversion with feet in it yes we do so we're going to

use that one and I'm gonna put one foot on the bottom

and 12 inches on the top and feet is on opposite division side so

it cancels so now we just have to go and put this in here so 120 3 over 1.

12 over 1 and we get four thousand three hundred and twenty inches

which should be our answer all right very good let's move on to the next one

okay backyard has an area of 43 560 feet squared um and notice how

this one's a little different um they already gave it to us in square feet

um so we don't need to square it we can just use it so that works out pretty nicely

so nine square feet or feet squared one yard squared and again feet squared is the same

on both sides so we can cancel that out so now we just need to go and do 43 560. 1 over 9.

and we get 4840. so 4840 square yards or yards

squared so just because you see the word square doesn't mean you necessarily have to

square it always check first if the unit conversion doesn't match you probably have to do something to it

um but we got lucky with this one they did match so we're all good all right question six

okay they weigh 220 pounds what's their Mass sash weight in kilograms okay so

we're gonna do if it's all right I'm gonna use abbreviations for this one G is grams kg is kilogram

so pounds do we have a unit conversion with pounds in it we do so we're going to use that one

gonna put one pound on the bottom 454 grams G on top

do pounds cancel they do we have grams but we don't want grams we want kilograms Let's cross this one out

because we're done using them and one kilogram equals a thousand grams so I'm going to put a thousand grams

on the bottom and one kilogram Kg on the top and grams is the same on both sides so

that cancels and we're left with kilograms which is what we want

so now we can go to the calculator and type in 220

454 over one one over one thousand and we get 99.88

kilograms or kg foreign

let's move on to question seven couple more left a tank is being emptied at 57 quarts per

hour okay let's write that down 57 quarts per hour

and Let's see we we have some mention of seconds and hours so we should probably

write down the other unit conversion that we need which is 3600

seconds equals one hour just use S for a second it doesn't matter you can write whatever you want

okay so why don't I do the chords first so I'm going to put one quart again so we have quartz so quartz is in

here so we're going to use that one so uh one quart and zero point

nine five liter and let's see I have quartz on opposite sides division sign so it cancels

and now we're going to kind of from across the way convert the hours so um let's see so I'm gonna put one hour

on the top and 3 600 seconds on the bottom hour is in opposite sides

of the division sign so it does cancel and we are left with liters per second which is what we wanted liters per

second so that looks really good so now we just have to type this all in and just

remember to round to the thousandth so um 57 0.95 over one

1 over 3600 and we get .015 that's the thousandth so

.015 liters per second very good

all right let's look at question eight so 85 93.5 square inches or inches squared

and I'm going to notice right away that there is no conversion factor with square inches it just has inch so we

have to do what we did before which is um we have to square both sides

of the unit conversion to get square units so we get 1 squared which is one inches squared

and 2.54 squared centimeter squared so that's actually

going to be our conversion factor and now we can do the factor label method

so I'm going to put 1 inches squared on the bottom and then 2.54 squared centimeters squared on the

top inches squared is on opposite sides division side so that's going to cancel

we're left with centimeters squared or square centimeters which is what we want so now we can jump to the calculator

and let's see what that is so at 93.5 [Music]

2.54 squared over one and it says to round to the 10th so I'm

going to say 603.2 looks like 603.2 centimeter squared or square

centimeters so just always make sure guys that you square or cube

the unit conversion accordingly if you have to all right that one looks good let me

just double check 603.2 yep let's get rid of all this all right two more

all right so we got 45 square yards per minute I'm going to use abbreviations again just to make it a little bit

easier for me so abbreviation for yard is yd squared so Square per

minute min uh so hmm interestingly enough it seems like we don't have square yards so this

is a rate unit conversion but it's also a square unit conversion so we have to do both

so um let's first Square both sides of this thing and we get 3 squared how about I just

make that nine because that comes out nicely and then 1 squared which is just one

yard squared so that's a conversion factor and then we also need to do minutes and seconds

so there are 60 Seconds in one minute that's just one we should

know let's write that down too okay let's get started so how about I do

the square yards first so one yard squared is going to go on the bottom and nine

feet squared is going to go on the top and yard squared is on opposite sides division sign so it cancels

and now we have feet squared per minute but we don't want feet squared permanent we want feet squared per second

so we're going to make another one and kind of convert the time from across the way

and I'm going to put one minute on the top 60 seconds at the bottom again if you

guess wrong guys just switch them you get a 50 50 chance of doing it right every time

um and uh let's see so now minutes is on opposite sides of division sign so um those guys cancel

and we're left with square feet per second which is what we want square feet per second

so we can now go to the calculator and let's see what that gives us so 45 parentheses 9 over 1.

parentheses 1 over 60 and we get 6.75 so six

0.75 feet squared per second and that is our answer

great let's look at question 10. a bathtub can hold a volume of 160 cubic decimeters

okay you guys don't need to know this but just to make it easier for me I'm going to write the abbreviation for

decimeters which is DM so n cubic remember we said that means to the third power the unit is to the

third power so I'm going to put DM cubed and I'm gonna look do I have cubic

decimeters in my conversion no I don't so I'm going to have to manipulate that guy

but instead of squaring it we're going to cube both sides so we get 3.05 cubed whatever that is

decimeters cubed equals 1 cubed which is just one feet cubed

and we're going to use that as our conversion factor and let's see so

3.05 cubed decimeters cubed is going to go on the bottom and then one feet cubed is going

to go on the top once again do the units cancel yes they do decimeters cubed is on both sides and

let's see we're left with feet cubed or cubic feet which is what we want so now we can go straight to the calculator

and do let's get rid of this we can do 160 parentheses 1 over

3.05 to the Third type in exactly as written and it wants us to round to the nearest tenth so I

guess that would be about 5.6 so 5.6 feet cubed or cubic feet is our answer

all right very good let's go back to the Whiteboard or I mean to the slides and wrap up

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