Converting Units With Conversion Factors - Metric System Review & Dimensional Analysis - By The Organic Chemistry Tutor
Transcript
00:0-1 | in this video , we're going to talk about how | |
00:02 | to convert from one unit into another . We're going | |
00:05 | to talk about units associated with distance , mass or | |
00:09 | weight , volume and capacity time , as well as | |
00:13 | units in the metric system . We're gonna cover that | |
00:15 | as well . So let's begin by taking some notes | |
00:21 | . Hopefully you have a sheet of paper with you | |
00:23 | and you may want to write down a few things | |
00:26 | . So let's begin with units associated with distance . | |
00:32 | You need to know that there's 12 inches in a | |
00:35 | foot three ft is equal to one yard , one | |
00:46 | inch is equivalent to 2.54 centimeters . One kilometer is | |
00:55 | equivalent to 1000 m . And these are some very | |
00:58 | common conversion factors that you might come across when dealing | |
01:02 | with unit conversion problems . Now there's more , one | |
01:07 | m is equal to 100 centimeters , one mile is | |
01:14 | equal to 1.609 kilometers and one mile is also equal | |
01:21 | to 5280 ft . So those are some conversion factors | |
01:28 | that you want to know when dealing with distance or | |
01:31 | less . Now let's talk about conversion factors associated with | |
01:35 | mass or weight . So here's the first common one | |
01:47 | that you'll see in chemistry . And even in physics | |
01:51 | , sometimes one kg is equal to 1000 g . | |
01:56 | one kg is also equivalent to £2.2 kilogram is a | |
02:04 | unit of mass , but pounds is typically a unit | |
02:07 | of weight . Even though you can convert from one | |
02:11 | to the other , they're not exactly the same . | |
02:13 | Embarrasses really a quantity of matter , whereas weight is | |
02:18 | a force , but you can convert from one to | |
02:21 | another . Now £1 is equal to 16 ounces . | |
02:31 | One ton is equal to £2000 and then there's a | |
02:38 | metric ton . This is not exactly the same as | |
02:43 | a regular ton , but a metric ton is equivalent | |
02:46 | to 1000 kg . It's also equal to approximately £2200 | |
02:54 | . And for those of you who want a more | |
02:55 | exact value , it's really 22 oh £4 . one | |
03:00 | kg is £2.204 . But you can use £2.2 around | |
03:05 | the value . So there's some common conversion factors that | |
03:10 | you want to be familiar when dealing with mass for | |
03:12 | weight . Now let's move on to the next topic | |
03:17 | . That is conversion factors for volume or capacity . | |
03:27 | One leader is equal to 1000 millilitres . One middle | |
03:34 | leader is equal to one cubic centimeter and the cubic | |
03:41 | meter is equal to 1000 leaders . One gallon is | |
03:49 | equal to 3.7 85 liters . A gallon is also | |
03:56 | equal to four quarts and one court is equal to | |
04:02 | two points . You may not need to know that | |
04:06 | one that's really not a common one , but sometimes | |
04:10 | you may see problems associated with it . Now let's | |
04:15 | talk about units of time . Many of you are | |
04:19 | aware of these units , So here's some common ones | |
04:24 | . One hour is equal to 60 minutes and there's | |
04:28 | 60 seconds in one minute , there's 24 hours in | |
04:34 | a day and there's approximately 365 days in the year | |
04:42 | . Now , if you're dealing with a leap year | |
04:45 | , which happens every four years , there is 366 | |
04:48 | days in a leap year . In that month , | |
04:52 | in the month of february , there's 29 days in | |
04:54 | a leap year , but in a regular year there's | |
04:56 | 28 days in the month of february . So keep | |
04:59 | that in mind . A typical calendar muff has an | |
05:03 | average of 30 days and one century is equal to | |
05:11 | 100 years . One millennium is equivalent to 1000 years | |
05:23 | . Now , let's go back to a leap here | |
05:26 | , which he said is 365 days . I mean | |
05:30 | 366 days rather because that happens every four years . | |
05:36 | If you were to average that in you get a | |
05:39 | typical year is more specifically 365 points 25 days . | |
05:47 | Some problems may require that you use the 0.25 days | |
05:51 | . Others may not . So you need to use | |
05:53 | your judgment whether you're going to use this conversion factor | |
05:56 | or that one . Either case , the answer shouldn't | |
06:00 | be that much different regardless of the two that you | |
06:03 | choose to use . But just keep in mind that | |
06:05 | small difference for some problems , it may be significant | |
06:12 | . Now let's talk about the metric system . You | |
06:19 | need to be able to write a conversion factor after | |
06:23 | you commit this to memory . So let's go over | |
06:27 | some things first . Terror is 10 to 12 Giger | |
06:33 | is 10 to 9 mega . It's 10 to 6 | |
06:39 | . As in kilo it's 10 to 3 Hector , | |
06:46 | 10 to the two and then deca it's 10 to | |
06:50 | the one and then you have your base unit . | |
06:52 | And then below that Desi is 10 to the minus | |
06:56 | one . And then since he 10 to the minus | |
06:59 | two millie 10 to the minus stream micro , that's | |
07:05 | 10 to minus six , nano is 10 to minus | |
07:09 | nine and Pickle is 10 to minus 12 . There's | |
07:14 | some other ones but typically you don't need to know | |
07:18 | the other ones that are outside of this range . | |
07:21 | If you do just look them up and you may | |
07:24 | want to write them down . There's some other ones | |
07:26 | like adult or fem two and I'll leave it to | |
07:29 | you to review that . But with this information you | |
07:32 | need to be able to write a conversion factor . | |
07:35 | So let's say if we want to write a conversion | |
07:37 | factor between meters and kilometers , so it's going to | |
07:43 | be one kilometer is equal to one times 10 to | |
07:47 | the third meters . So here's how you can set | |
07:50 | up the conversion factors . Always put a one next | |
07:55 | to the side of the equation that has the prefix | |
07:57 | such as kilo , terra giga , mega or micro | |
08:02 | , and then place the multiplier near the base unit | |
08:05 | meters seconds . Watch whatever it may be . So | |
08:11 | let me give you some examples . One gigawatt is | |
08:16 | equal to one times 10 to 9 watts . Let | |
08:22 | me remove this . Hopefully you wrote that down . | |
08:27 | A mega jaw is equal to one times 10 to | |
08:33 | the sixth jewels one centimeter since he is 10 to | |
08:38 | the minus two , So one centimeter is gonna be | |
08:41 | one times 10 to the minus two m . A | |
08:45 | nanosecond , nano is 10 to minus nine , so | |
08:49 | it's going to be one times 10 to minus nine | |
08:52 | seconds . A micro meter is one times 10 to | |
09:00 | minus six m . So once you commit this to | |
09:05 | memory , it's going to be very easy for you | |
09:10 | to write the conversion factor which will make it easier | |
09:14 | to solve problems associated with converting units with the metric | |
09:18 | system . So make sure you write this down . | |
09:22 | So let's start with some simple problems . Let's say | |
09:26 | we wish to convert four ft into inches . How | |
09:31 | can we do so ? Well this is a one | |
09:34 | step conversion . We need to write the conversion factor | |
09:38 | that helps us to go from feet two inches . | |
09:41 | So if you recall it is one ft is equal | |
09:46 | to 12 inches . This is our conversion factor . | |
09:50 | So that's the first thing you wanna do , identify | |
09:53 | what conversion factors will help you to do the problem | |
09:58 | . Once you do that , start with what you're | |
10:00 | given . So were given four ft , we're going | |
10:02 | to put that over one . Now let's write another | |
10:06 | fraction . Now we need to determine what to put | |
10:10 | in this fraction . Should we put the 12 inches | |
10:15 | on the top of the fraction or in the bottom | |
10:17 | of the fraction ? In order for this to work | |
10:21 | ? We neither units feet to cancel . So because | |
10:25 | it's on the top in the first fraction , we | |
10:27 | want to put feet in the bottom of the second | |
10:30 | fraction on top of the first fraction , we're going | |
10:33 | to put interests and then we're just gonna put the | |
10:35 | numbers associated next to it . So we have a | |
10:38 | one next defeat and the 12 next two inches . | |
10:42 | So these units will cancel . And now we just | |
10:44 | need to do the math . So whenever you see | |
10:47 | two numbers on top multiplied by those numbers . For | |
10:51 | numbers on the bottom you're gonna divide by that number | |
10:54 | . Four times 12 is 48 . So the answer | |
10:57 | is 48 inches . four ft is equivalent to 48 | |
11:01 | inches . So that's how you can convert from one | |
11:04 | unit to another . Now let's try some more examples | |
11:08 | with one step conversion problems . Go ahead and convert | |
11:14 | 350 g into kilograms and also convert 0.45 leaders into | |
11:28 | mid leaders . So feel free to pause the video | |
11:32 | and work on these examples . And then once you | |
11:35 | finish working on them , play the video to see | |
11:38 | if you have the right answer . So let's start | |
11:42 | the first one . The first thing we need to | |
11:45 | do is identify the conversion factor between grams and kilograms | |
11:51 | . Now we wrote this down earlier , one kg | |
11:58 | is equal to 1000 gramps . So that's a conversion | |
12:05 | factor . So using that , how can we convert | |
12:10 | 350 g into kilograms . Feel free to work on | |
12:18 | that . Mhm . So the first thing you want | |
12:22 | to do is you want to start with what you're | |
12:23 | given that is 350 g over one . Then you | |
12:28 | need to decide what to put on the next fraction | |
12:31 | . So because we have the unit grams here , | |
12:33 | we want to put grams on the bottom kilograms on | |
12:37 | top . The number associated with kilograms is one . | |
12:42 | The number associated with grabs is 1000 . So when | |
12:49 | we set it up this way we can see that | |
12:51 | the unit grams will cancel now because this number is | |
12:54 | on the bottom , we're going to divide 3 50 | |
12:57 | by 1000 3 50 divided by 1000 is point 35 | |
13:05 | kilograms . Another way in which you can conveniently divide | |
13:09 | by 1000 is you can move the decimal three units | |
13:13 | to left . So that's the answer for the first | |
13:18 | example . Now let's move on to the second example | |
13:23 | . So this is another one step conversion problem but | |
13:26 | here we're dealing with volume as opposed to mass . | |
13:30 | Now the first thing we need to do is we | |
13:32 | need to write the conversion factor . What is the | |
13:35 | conversion factor between leaders and milliliters ? As you mentioned | |
13:42 | earlier in this video , one leader is equal to | |
13:45 | 1000 mL . So that's the conversion factor that we're | |
13:49 | going to use . Now let's start before were given | |
13:53 | 0.45 liters since we have leaders on the top , | |
13:57 | we're going to put that on the bottom and then | |
13:59 | we're gonna put the other unit mid leaders on top | |
14:03 | , there's a one in front of leaders and there's | |
14:06 | 1000 in front of me leaders . So this time | |
14:11 | we need to multiply by 1000 instead of dividing by | |
14:14 | 1000 because these two numbers are on the numerator of | |
14:17 | the fractions . So 0.4 me . Say that again | |
14:20 | ? 0.45 times 1000 . That's going to be 450 | |
14:26 | . So when whenever you multiply by 1000 move the | |
14:29 | decimal three units to the right , if you divide | |
14:32 | by 1000 you want to move the decimal three units | |
14:34 | to left . Likewise , if you were to multiply | |
14:37 | by 100 you can just move the decimal two units | |
14:40 | to the right . If you were to divide by | |
14:42 | 100 move it to units to the left . So | |
14:47 | here the unit Leaders council and now we have our | |
14:50 | final answer which is 450 mL . Now let's work | |
14:55 | on some board problems . If Karen can make seven | |
14:59 | cakes in three hours , how many cakes can she | |
15:02 | make in 10 hours , feel free to work on | |
15:05 | this example problem . So this is another one step | |
15:10 | conversion problem . But the first thing is , what | |
15:14 | is the conversion factor and what are we trying to | |
15:16 | do here ? Right now ? We want to convert | |
15:21 | time into cakes , so to speak , were given | |
15:26 | at the time of 10 hours and we want to | |
15:31 | know how many cakes can she make . Now in | |
15:38 | order to find the answer , we need to identify | |
15:41 | the conversion factor . So now that we've identified the | |
15:44 | problem , what is the conversion factor ? The conversion | |
15:48 | factor is basically in this example the rate in which | |
15:51 | she can make cakes , she can make seven cakes | |
15:55 | in three hours . So to keep things simple we're | |
15:58 | gonna say seven cakes is equal to three hours . | |
16:02 | So now let's convert let's start with what we're given | |
16:06 | , which is 10 hours , we're gonna put that | |
16:09 | over one and then we're going to convert that to | |
16:11 | the number of cakes that she can make . So | |
16:15 | because we have hours on top , we're going to | |
16:17 | put hours on the bottom and then cakes on top | |
16:22 | and then we're going to use our conversion factor here | |
16:26 | . So there's a three in front of ours , | |
16:29 | a seven in front of cakes and now we can | |
16:32 | do the math . So it's going to be 10 | |
16:34 | times seven , which is 70 divided by three . | |
16:43 | Now let's get a calculator to convert this to a | |
16:46 | decimal 70 divided by three is 23.3 repeating . So | |
16:56 | that's how many cakes she can make in 10 hours | |
17:01 | . Now let's move on . And number two , | |
17:04 | a certain map has the following scale one inch is | |
17:08 | equal to 5.5 miles . If the distance between city | |
17:12 | abc and City X , Y Z is 12.6 inches | |
17:16 | on the map , what is the distance in miles | |
17:19 | between the two cities ? So feel free to pause | |
17:24 | the video and uh try that example . Now we | |
17:28 | need to identify the problem . What is it that | |
17:31 | we're trying to do here ? What we want to | |
17:35 | do is were given the distance between the two cities | |
17:40 | , which is in inches more specifically interest on the | |
17:44 | map . We want to convert that into an actual | |
17:48 | distance in mouse . So we want to go from | |
17:52 | inches to mouse . But in order to do it | |
17:56 | right or get the right answer , we need to | |
17:59 | use the conversion factor that's given to us based on | |
18:05 | the scale that's on the map . So for this | |
18:08 | problem , not for other problems . One inch is | |
18:11 | equal to 5.5 miles . So this is a one | |
18:14 | step conversion problems . So we're given 12.6 inches . | |
18:20 | We want to convert that to mouse . So let's | |
18:22 | start with what we're given and then let's use our | |
18:29 | conversion factor to complete the second fraction . So we | |
18:33 | have inches on top , we're going to put inches | |
18:35 | on the bottom and so my house is going to | |
18:36 | go on top , there's a one in front of | |
18:39 | inches and 5.5 in front of my house . So | |
18:45 | all we need to do for this problem is multiply | |
18:48 | 12 26 by 5.5 and so we're going to get | |
18:57 | 69.3 mouse . So based on the scale that were | |
19:01 | given this is the distance in mouse between the two | |
19:05 | cities . Now let's talk about how we can solve | |
19:10 | a two step conversion problem . Let's say we want | |
19:14 | to convert from inches two yards , how can we | |
19:18 | do so how many yards is equivalent to 180 inches | |
19:25 | . Feel free to pause the video and try that | |
19:28 | . So let's write down some conversion factors that we | |
19:32 | know , we know that there's three ft in the | |
19:35 | yard and there's 12 inches in the foot . So | |
19:44 | these are the two conversion factors that we need to | |
19:47 | go from inches to the arts . So we're gonna | |
19:49 | start with inches , and then we're going to convert | |
19:52 | that to feet using this conversion factor , and then | |
19:57 | once we have feet we can convert feet two yards | |
20:01 | using this conversion factor . So let's begin , let's | |
20:05 | start with what we're given . And that is 180 | |
20:09 | inches over one next . Since we have inches on | |
20:13 | top , we're gonna put interest on the bottom and | |
20:17 | then we're going to put feet on top . So | |
20:20 | using the first conversion factor , we know that there's | |
20:24 | 12 inches in a foot . So we're going to | |
20:27 | use , we're gonna put the same numbers next to | |
20:30 | the correspondent units . So now the units inches will | |
20:34 | cancel . And here we have units of feet . | |
20:37 | So now we're gonna go from feet to yards using | |
20:40 | this one . So since we see the unit feet | |
20:44 | on top , we're going to put feet on the | |
20:45 | bottom , the yards on top , there's a one | |
20:48 | in front of yards , three in front of feet | |
20:54 | , and then we can cross out those units . | |
20:57 | So it's going to be 180 divided by 12 . | |
21:02 | Let's do this one step at a time . So | |
21:05 | 1 80 divided by 12 is 15 and then we're | |
21:09 | gonna take 15 divided by three , which will give | |
21:13 | us five . So the final answer is five yards | |
21:22 | . Try this one , Go ahead and convert 9000 | |
21:25 | ft into kilometers . So what conversion factors do we | |
21:36 | need in order to go from feet two kilometers first | |
21:40 | , let's make an outline of what we need to | |
21:41 | do because this is another two step conversion factor or | |
21:45 | two step conversion problem . Now we know the conversion | |
21:48 | factor that will take us from feet to mouse and | |
21:52 | then we know the one that's gonna take us from | |
21:53 | miles to kilometers . So we know that there's one | |
21:58 | , well we know that one mile is equal to | |
22:00 | 5280 ft and one mile is also equal to 1.609 | |
22:09 | kilometers . So let's start with what we're given , | |
22:17 | were given 9000 ft , let's put that over one | |
22:21 | . And let's use our first conversion factor to go | |
22:24 | from feet to mouse . So 5280 ft is equal | |
22:32 | to one mouth , so we can cross out those | |
22:35 | units . And then let's use the second conversion factor | |
22:41 | to go from miles to kilometers . One mouth is | |
22:46 | equal to 1.609 kilometers . So remember divide by the | |
22:55 | numbers on the bottom , multiplied by the numbers on | |
22:58 | top . So it's going to be 9000 , divided | |
23:03 | by 50 to 80 and then take that result multiplied | |
23:07 | by 1.69 So the final answer is going to be | |
23:11 | 2.7 4 to 6 kilometers . So that's equal to | |
23:20 | 9000 ft . Here's another example . Let's convert 7500 | |
23:27 | mL , two gallants . So what are some conversion | |
23:34 | factors that we could use here ? Well , first | |
23:38 | , let's make an outline . We know the one | |
23:40 | that's gonna take us from the leaders to leaders , | |
23:43 | and we have one that can take us from Leaders | |
23:45 | two gallons . So for the first step we could | |
23:47 | use this one , we know that one leader is | |
23:51 | equal to 1000 millimeters . And for the second step | |
23:53 | we could use the fact that one gallon is equal | |
23:57 | to 3.785 leaders . So let's start with what we're | |
24:03 | given . And that is 7500 mL over one . | |
24:10 | So let's use the first conversion factor to go from | |
24:14 | middle leaders to leaders . So we're gonna put 1000 | |
24:16 | mL on the bottom so that these units will cancel | |
24:21 | . And then one leader on top . Now let's | |
24:28 | use the second conversion factor to go from leaders two | |
24:31 | gallons . So we're going to put 3.7 85 liters | |
24:37 | on the bottom and then one gallon on top . | |
24:44 | So now it's going to be 7500 , divided by | |
24:46 | 1000 which is 7.5 and then divide that by 3.75 | |
24:54 | . So the answer , it's equal to 1.98 gallons | |
25:01 | . So this is an example of converting from one | |
25:04 | unit of volume to another . So that's how you | |
25:07 | can convert from milliliters , two gallons number three . | |
25:12 | A book weighs £7.12 ounces . What is the mass | |
25:17 | of the book in kilograms ? So what do you | |
25:20 | think we need to do for this one ? Well | |
25:24 | , we need to convert pounds , announces two kg | |
25:30 | . So the book has a weight of £7 and | |
25:36 | or plus 12 ounces . What we need to do | |
25:40 | is we need to convert pounds to kilograms and then | |
25:44 | ounces two kg and then get the sum total of | |
25:47 | that answer and then we'll get the mass of the | |
25:49 | book in kilograms . So let's convert pounds to kilograms | |
25:55 | first to do that . What conversion factor do we | |
26:05 | need ? So if you recall , one kg is | |
26:11 | equal to £2.2 . So that's the conversion factor we | |
26:15 | need for the first part . So let's start with | |
26:20 | £7 over one . And then in the next fraction | |
26:25 | we're going to put £2.2 on the bottom , one | |
26:29 | kg on top . So here we need to divide | |
26:33 | so it's going to be seven divided by 2.2 . | |
26:42 | And so you get 3.18 repeating , but I'm going | |
26:45 | around it to 3.182 kilograms . So that's the first | |
26:53 | part . So now let's convert ounces 12 ounces , | |
26:58 | two kg . In this case this is a two | |
27:02 | step process . We need to go from ounces £2 | |
27:09 | and then we can go from pounds to kilograms . | |
27:14 | So let's start with 12 ounces . Now what is | |
27:22 | the conversion factor between ounces and pounds ? Just looking | |
27:27 | at the notes , we know that £1 is equal | |
27:31 | to 16 ounces . So that's the conversion factor that | |
27:35 | we need to use right now . So I'm going | |
27:39 | to put 16 ounces on the bottom , £1 on | |
27:43 | top . So now we could cancel the unit ounces | |
27:51 | and then we could use this conversion factor to go | |
27:53 | from pounds to kilograms . So I'm gonna put £2.2 | |
27:57 | on the bottom one kg on top . So it's | |
28:05 | going to be 12 divided by 16 , which is | |
28:09 | 160.75 And then divide that by 2.2 , which is | |
28:13 | 0.341 kg . So £7 is equal to 3.182 kg | |
28:22 | . 12 ounces is equal 2.341 kg . The book | |
28:27 | weighs £7.12 ounces . So to get the mass , | |
28:30 | we just need to are these two numbers . So | |
28:34 | 3.182 plus 0.341 This will give us a total mass | |
28:40 | of 3.5 23 kg . So that's the mass of | |
28:45 | the book in this example . Now let's move on | |
28:49 | to number four . One box can hold 28 cupcakes | |
28:53 | , and five cups of flour are required to make | |
28:55 | three cupcakes . How many cups of flour are required | |
28:58 | to make enough cupcakes to fill 12 boxes . So | |
29:05 | what do we need to do here ? Well , | |
29:07 | let's identify the problem first . We need to convert | |
29:11 | 12 boxes . Two , The number of cups of | |
29:17 | flour . So I'm just gonna write cups . That's | |
29:22 | what we're given . 12 boxes . And the question | |
29:24 | says , how many cups of flour are required to | |
29:27 | make enough cupcakes to fill those tall boxes ? So | |
29:30 | we got to convert 12 boxes , two cupcakes . | |
29:34 | Now , we need to write our conversion factors were | |
29:38 | given the first one . One box can hold 28 | |
29:41 | cupcakes . So we're gonna write one box is equal | |
29:44 | to 28 cupcakes . And then we have our second | |
29:54 | conversion factor . Five cups of flour are required to | |
29:59 | make three cupcakes . So what we're gonna do is | |
30:09 | first we're gonna start with boxes and then we're going | |
30:13 | to convert that to cupcakes . And once we have | |
30:17 | cupcakes we're going to convert that two cups of flour | |
30:24 | . So let's begin , let's start with what we're | |
30:26 | given were given 12 boxes , We're going to put | |
30:30 | that over one . And then we're gonna convert from | |
30:34 | boxes , two cupcakes . So we need to use | |
30:37 | this conversion factor so one box can hold 28 cupcakes | |
30:48 | . And then for the second step , we need | |
30:51 | to convert cupcakes , two cups of flour using this | |
30:55 | conversion factor . So I'm gonna put three cupcakes on | |
30:59 | the bottom and then five cups of flour on top | |
31:09 | . So the unit boxes cancels as well as cupcakes | |
31:14 | . So now we just got to do the math | |
31:15 | . It's gonna be 12 times 28 which is 3 | |
31:21 | 36 times five , which is 16 80 divided by | |
31:26 | three . So that's 560 . So 560 cups of | |
31:35 | flour are required to make 12 boxes each with 28 | |
31:42 | cupcakes . So that's the final answer for this problem | |
31:49 | . Now , let's focus on the metric system . | |
31:52 | Let's work on example , problems using the metric system | |
31:56 | , Let's say we want to convert 38.6 millimeters to | |
32:02 | meters . How can we use the metric system to | |
32:05 | do this ? Now this is a one step problem | |
32:10 | . But what we need to do is identify what | |
32:12 | the conversion factor is . So the key word is | |
32:18 | millie . If you recall , Millie is associated with | |
32:22 | tents and monastery . Therefore , to write the conversion | |
32:25 | factor , we can say one millimeter is equal to | |
32:28 | one times 10 to minus three m . And this | |
32:32 | step is important . We cover this early in the | |
32:34 | video . As long as you can write the conversion | |
32:36 | factor for the metric system , solving these problems won't | |
32:39 | be too hard . So now we can convert . | |
32:44 | So we're gonna start with 38.6 millimeters over one and | |
32:49 | then we're gonna put the unit millimeters on the bottom | |
32:52 | and then the unit meters on top . So now | |
33:00 | we need to multiply . So here we have 38 | |
33:04 | . Let me say that again . 38.6 times one | |
33:07 | and then times 10 to the ministry , which is | |
33:11 | 38.6 times 10 to minus three m . Now we | |
33:17 | want to put this in proper scientific notation . So | |
33:22 | what we need to do is we need to move | |
33:23 | the decimal 0.1 , unit two left . We wanted | |
33:25 | to be in front of the first two numbers . | |
33:28 | So this is going to be 386 And whenever you | |
33:32 | move it to the left this number is going to | |
33:35 | increase by one . So it's gonna go from negative | |
33:38 | 32 negative two . So this right here is the | |
33:43 | answer is 3.86 times 10 to the minus two . | |
33:48 | And of course you can just put this in the | |
33:49 | calculator . If you type in 38.6 times one time | |
33:52 | since the ministry it will give you 0.386 metres , | |
34:00 | which is the same as 3.86 times 10 to minus | |
34:04 | student . So hopefully you're familiar with scientific notation . | |
34:07 | If not I do have a video on that which | |
34:10 | will help you whatever you see things like this . | |
34:15 | Now let's work on a two step conversion problem using | |
34:20 | the metric system . So let's say we have 49 | |
34:23 | 50 PICO meters and we want to convert that to | |
34:27 | nanometers . Go ahead and work on this problem . | |
34:33 | So what is the conversion factor for people ? Meters | |
34:36 | ? We know that PICO is 10 to minus 12 | |
34:40 | , so we can say one PICO meter is one | |
34:43 | times 10 to the negative 12 m and nano is | |
34:48 | 10 to minus nine , so one nanometer is one | |
34:52 | times 10 to minus nine m . So those are | |
34:56 | the two conversion factors that we need . So what | |
34:58 | we're gonna do is we're gonna start from p kilometers | |
35:01 | , we're going to convert it some meters and then | |
35:03 | meters , two nanometers . So let's begin , let's | |
35:06 | start with what we're given 49 50 p kilometers over | |
35:10 | one . And then let's convert that two m . | |
35:14 | So let's use this conversion factor . So we have | |
35:20 | one PICO meter and then one times 10 to minus | |
35:24 | 12 m . So we can cross out these two | |
35:28 | units . Now using the second conversion factor , let's | |
35:37 | convert meters , two nanometers , so we're gonna put | |
35:40 | meters on the bottom and then nanometers on top . | |
35:48 | So now let's do the math first . Let's see | |
35:54 | if we can do this mentally . Let's take the | |
35:58 | 10 to the negative nine and let's move it to | |
36:00 | the top . By the way , one over X | |
36:04 | to the monastery is the same as X to the | |
36:07 | positive three . Whenever you move a variable from the | |
36:11 | denominator numerator , the exponent changes side . So in | |
36:16 | this case it's going to change from negative nine to | |
36:18 | positive nine . So what we have is 49 50 | |
36:23 | times 10 to minus 12 times tends to positive nine | |
36:29 | . Now let's review some rules in algebra rules associated | |
36:33 | with exponents . If we multiply X to the fourth | |
36:36 | by exit fifth , this is going to be equal | |
36:39 | to exit a knife whenever you multiply by a common | |
36:43 | base or to common variables , the exponents should be | |
36:48 | added . So here the common bases 10 and we're | |
36:53 | multiplying them . So we're going to add negative 12 | |
36:56 | and nine which will give us negative three . So | |
36:59 | what we have now is 49 50 times 10 to | |
37:03 | the negative three . And of course we have the | |
37:06 | units nanometers . Now we need to put this in | |
37:10 | proper scientific notation form , so we're gonna move the | |
37:15 | decimal three units to left . We want the dismal | |
37:18 | to be between the first to non zero numbers . | |
37:23 | So here's some things you want to keep in mind | |
37:25 | whenever you need to move the decimal and whenever you're | |
37:28 | adjusting the exponents , if you move the decimal two | |
37:31 | left the export on 10 increases . If you move | |
37:35 | the decimal to the right , the exported on 10 | |
37:37 | decreases . So since we moved it three units alef | |
37:42 | , we're going to add 32 negative three , so | |
37:45 | we're going to get 4.95 times tends to zero and | |
37:50 | anything raised zero power is one , so 4.95 times | |
37:55 | one is just 4.95 So this is our final answer | |
37:59 | is simply 4.95 nanometers and you can take this in | |
38:04 | your calculator . If you type in 49 50 times | |
38:06 | one times 10 to minus 12 and then divided by | |
38:10 | one times 10 to minus nine , you're going to | |
38:13 | get 4.95 So this is the right answer . |
Summarizer
DESCRIPTION:
OVERVIEW:
Converting Units With Conversion Factors - Metric System Review & Dimensional Analysis is a free educational video by The Organic Chemistry Tutor.
This page not only allows students and teachers view Converting Units With Conversion Factors - Metric System Review & Dimensional Analysis videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.