Unit Conversion & Dimensional Analysis

Hello everyone, here is another video with OrgTube channel. In this video, I'm going to talk about unit conversion and dimensional analysis. I'm going to explain this concept by a series of examples. The first example, we want to convert 8.7 inches. into centimeter and the question already provide this information that one inch is equal to 2.54 if I write one inch is equal to 2.54 centimeter I can divide both side of this equation by one of these two value if I write one inch on both side then on the left side these two inch they cancel out then i get this equation one is equals to 2.54 centimeter over one inch this fraction called conversion factor conversion factor is equals to one so if i multiply conversion factor to any numbers the value of that quantity doesn't change. In this case I would like to use it for conversion of 8.7 inch to centimeter. When I write 8.7 inch I can multiply it by this conversion factor and always when we use conversion factor we need to use it in such a way that the units they can cancel out. In this case inch here and inch on denominator they cancel out and on nominator we have 2.54 centimeter as a result here the answer is 8.7 times 2.54 and the unit converts to centimeter so we don't have inch anymore and the answer is equals to 22 centimeter Please keep in mind that some of these numbers in conversion factor, they are exact numbers and they have infinite significant figure. One of these example is 2.54 cm. So this is one way for using this information. Let's say we want to convert cm to inch. Let's say we have 15 cm and we want to convert it to the inch. Then when we multiply by conversion factor, we should have centimeter at the bottom here. And we should have inch because always the unit is supposed to cancel out. And based on this value, we know 1 inch is equal to 2.54 centimeter. And we can have our answer. But why we can do that? because at the beginning instead of dividing both sides by one inch i could divide both of them by 2.54 centimeter then i had this conversion factor as well 2.54 at the bottom and one inch on top so for each information we can have two different conversion factor It's different to the question which one we have to use in our solution. In this case, the answer is 15 over 2.54 and the unit is inch, which is equal to 5.9 inch. Let's have more examples. Here is the next example. we would like to convert 0.2640 kilogram into gram so our given information is this and we should have a conversion factor and here we should have kilogram so they can cancel out and here we should have gram let's find out what are these numbers to find these numbers in conversion factor we should know that kilo it means thousand or ten to positive three So when we write 1 kilogram it means 1000 gram. So we can use these values for conversion factor. Here we can have 1000 gram. equals to 1 kilogram and kilogram and kilogram they cancel out and the answer is 264 gram this thousand it is again an exact number and we just ignore it when we have calculation with significant figures this number has four significant figure and our final answer should have for significant figure as well. Let's have more example. The next question we would like to convert 0.354 liter into microliter. So our conversion factor should have liter here and should have microliter. And we should know that micro is 10 to power of negative 6. So when I write 1 microliter. Micro is means 10 to negative 6. Then leader is just we have the same unit. So if I write 1 here I should have 10 to negative 6 here. Then we can have our answer. The answer is 0.354 over 10 to negative 6. We know if we take this to nominate the negative 6 converts to positive 6 and our final answer is 0.354 times 10 to positive 6 or if i convert it to the scientific notation form it is equal to 3.54 times 10 to positive 5 micro leader Here is the next example. In many examples like this example we may need to use more than one conversion factor. We would like to convert mile into inch but we don't have a conversion factor directly between mile and inch. We have mile to foot and we have foot to inch. So we should have two conversion factor 2.5 mile times We have this information in our question. One mile is equals to 52 AD foot. So I should write mile here so it can cancel out with this mile and on top write 52 AD feet. Right now the unit is foot and we have another conversion factor foot and inch. Then for next conversion factor, I should have foot here. Then this foot and this foot, they can cancel out. So one foot is 12 inch. Right now, the unit in this calculation is inch. And what is remaining here is 2.5 times 52 AD. times 12 and both of these 5280 and 12 again they are exact number and we just ignore them in our calculation for significant figure the answer from calculator is 158 400 inch and if we want to consider that we actually should consider the significant figure rules We have two significant figures and we need to run this number to two significant figures. So we should write the answer is. Let's have more examples. In this example we would like to convert the speed of car from kilometer per hour into meter per second. So 79.2 kilometer per hour. both of this unit they should convert kilometer to meter and hour to second so we need to use two conversion factor first i'm going to convert kilometer to meter so i should have kilometer here then they can cancel out one kilometer it should be 1000 meter so right now we have the meter for our unit in final answer But we need to also change hour into second. For hour because it is here on denominator then in conversion factor it should be opposite and we should have it Here then they can cancel out and at the bottom here I should have second We know one hour is equals to 60 minute and one minute is Equals to 60 second. So one hour is equals to 3600 Second and write 3600 Second here Right now the unit for our answer it is meter per second and then we can have this calculation. We have 79.2 times 1000 and on denominator we have 3600. These two zeros they can cancel out and then the answer is equals to 22. meter per second. Here is the next question. In this question we would like to find out how many square centimeter are there in 0.951 square meter. Our unit here it has power and let's find out how we can solve this question. So here is the given information. square meter times we need to convert meter to centimeter but we also have a power so we know one centimeter is equal to 10 to negative 2 meter because centi is means 10 to negative 2 or we may also sometimes see that 100 centimeter is equal to 1 meter because if we multiply in both by 100 we can get the second conversion factor we should have meter here and centimeter here then based on this conversion factor i know that one centimeter is 10 to negative 2 meter but this meter and square meter they don't cancel each other and we know the value for conversion factor is always equals 1 And it doesn't matter if we have 1 or 1 square or 1 cube. All of them, they have the same value. So I can put any power I need during the calculation for any conversion factor. In this case, I need the s square. So I put 2 here. Then if I rewrite this equation, actually we have m square here times. then one square still is one then we have a square centimeter then 10 to negative 2 square will be 10 negative 4 right now they cancel out and our unit is a square centimeter the answer is equals to 0.951 over 10 negative 4 And again, we can take this to nominator and have 951 times 10 to positive 4. Or, converted to the scientific notation, the answer is 9.51 times 10 to positive 3 square centimeter. In this example, we would like to convert 1.2 liter into cubic feet. At the beginning, it seems we don't have the conversion factor we need that. But conversion of liter into cubic meter is a very famous conversion factor and everybody needs to know that. 1000 liter is equal to 1 cubic meter. So 1.2 liter times here at the bottom I should have liter so then thousand liter liter and liter they can cancel out and here is one cubic meter. Then we have the information from the question that one meter is equals to 3.28 feet so one meter 3.28 feet. And here the power for our unit is 3. And here the power is 1. So I need to put the whole conversion factor to the power 3. Then let's rewrite this over 1000 times. Here we have 1 cubic meter. Then feet converts to cubic feet. And 3.28 it should also have a power 3. Then we can have our final answer. 1.2 times 3.28 to power of 3 is equal to 3529 cubic feet and at denominator we have 1000. This 1000. The final answer is equal to 0.042 cubic feet. And here is the last example. We would like to find out how many years do we have in 6.57 times 10 to positive 6 minutes. So let's write 6.57 times 10 to positive 6 minutes. So to convert it to the year we need to convert minutes into hour, hour into days. days into years and we know all of these conversion factor so first I'm going to convert minute to hour we know 60 minute is equals to one hour so minutes and minutes they cancel out then the next conversion factor is hours into the day so we know 24 hours is one day then hour and hour they cancel out and then we know each year is 365 days it has a little bit more than that you just simply assume is 365 so 365 day is one year and day and day also they can sell out. so all we have right now is just these numbers 6.57 times to 10 positive 6 here we have 1 1 1 so we don't have anything else for nominator but on denominator we have 60 we have 24 and we have 365. the answer is equals to 12 point five year thank you for watching this video to watch more video please make sure to subscribe to this channel

Hello everyone, here is another video with OrgTube channel. In this video, I'm going to talk about unit conversion and dimensional analysis. I'm going to explain this concept by a series of examples.

The first example, we want to convert 8.7 inches. into centimeter and the question already provide this information that one inch is equal to 2.54 if I write one inch is equal to 2.54 centimeter I can divide both side of this equation by one of these two value if I write one inch on both side then on the left side these two inch they cancel out then i get this equation one is equals to 2.54 centimeter over one inch this fraction called conversion factor conversion factor is equals to one so if i multiply conversion factor to any numbers the value of that quantity doesn't change. In this case I would like to use it for conversion of 8.7 inch to centimeter.

When I write 8.7 inch I can multiply it by this conversion factor and always when we use conversion factor we need to use it in such a way that the units they can cancel out. In this case inch here and inch on denominator they cancel out and on nominator we have 2.54 centimeter as a result here the answer is 8.7 times 2.54 and the unit converts to centimeter so we don't have inch anymore and the answer is equals to 22 centimeter Please keep in mind that some of these numbers in conversion factor, they are exact numbers and they have infinite significant figure. One of these example is 2.54 cm.

So this is one way for using this information. Let's say we want to convert cm to inch. Let's say we have 15 cm and we want to convert it to the inch.

Then when we multiply by conversion factor, we should have centimeter at the bottom here. And we should have inch because always the unit is supposed to cancel out. And based on this value, we know 1 inch is equal to 2.54 centimeter.

And we can have our answer. But why we can do that? because at the beginning instead of dividing both sides by one inch i could divide both of them by 2.54 centimeter then i had this conversion factor as well 2.54 at the bottom and one inch on top so for each information we can have two different conversion factor It's different to the question which one we have to use in our solution.

In this case, the answer is 15 over 2.54 and the unit is inch, which is equal to 5.9 inch. Let's have more examples. Here is the next example. we would like to convert 0.2640 kilogram into gram so our given information is this and we should have a conversion factor and here we should have kilogram so they can cancel out and here we should have gram let's find out what are these numbers to find these numbers in conversion factor we should know that kilo it means thousand or ten to positive three So when we write 1 kilogram it means 1000 gram.

So we can use these values for conversion factor. Here we can have 1000 gram. equals to 1 kilogram and kilogram and kilogram they cancel out and the answer is 264 gram this thousand it is again an exact number and we just ignore it when we have calculation with significant figures this number has four significant figure and our final answer should have for significant figure as well.

Let's have more example. The next question we would like to convert 0.354 liter into microliter. So our conversion factor should have liter here and should have microliter.

And we should know that micro is 10 to power of negative 6. So when I write 1 microliter. Micro is means 10 to negative 6. Then leader is just we have the same unit. So if I write 1 here I should have 10 to negative 6 here.

Then we can have our answer. The answer is 0.354 over 10 to negative 6. We know if we take this to nominate the negative 6 converts to positive 6 and our final answer is 0.354 times 10 to positive 6 or if i convert it to the scientific notation form it is equal to 3.54 times 10 to positive 5 micro leader Here is the next example. In many examples like this example we may need to use more than one conversion factor. We would like to convert mile into inch but we don't have a conversion factor directly between mile and inch.

We have mile to foot and we have foot to inch. So we should have two conversion factor 2.5 mile times We have this information in our question. One mile is equals to 52 AD foot. So I should write mile here so it can cancel out with this mile and on top write 52 AD feet.

Right now the unit is foot and we have another conversion factor foot and inch. Then for next conversion factor, I should have foot here. Then this foot and this foot, they can cancel out.

So one foot is 12 inch. Right now, the unit in this calculation is inch. And what is remaining here is 2.5 times 52 AD. times 12 and both of these 5280 and 12 again they are exact number and we just ignore them in our calculation for significant figure the answer from calculator is 158 400 inch and if we want to consider that we actually should consider the significant figure rules We have two significant figures and we need to run this number to two significant figures. So we should write the answer is.

Let's have more examples. In this example we would like to convert the speed of car from kilometer per hour into meter per second. So 79.2 kilometer per hour. both of this unit they should convert kilometer to meter and hour to second so we need to use two conversion factor first i'm going to convert kilometer to meter so i should have kilometer here then they can cancel out one kilometer it should be 1000 meter so right now we have the meter for our unit in final answer But we need to also change hour into second. For hour because it is here on denominator then in conversion factor it should be opposite and we should have it Here then they can cancel out and at the bottom here I should have second We know one hour is equals to 60 minute and one minute is Equals to 60 second.

So one hour is equals to 3600 Second and write 3600 Second here Right now the unit for our answer it is meter per second and then we can have this calculation. We have 79.2 times 1000 and on denominator we have 3600. These two zeros they can cancel out and then the answer is equals to 22. meter per second. Here is the next question. In this question we would like to find out how many square centimeter are there in 0.951 square meter.

Our unit here it has power and let's find out how we can solve this question. So here is the given information. square meter times we need to convert meter to centimeter but we also have a power so we know one centimeter is equal to 10 to negative 2 meter because centi is means 10 to negative 2 or we may also sometimes see that 100 centimeter is equal to 1 meter because if we multiply in both by 100 we can get the second conversion factor we should have meter here and centimeter here then based on this conversion factor i know that one centimeter is 10 to negative 2 meter but this meter and square meter they don't cancel each other and we know the value for conversion factor is always equals 1 And it doesn't matter if we have 1 or 1 square or 1 cube.

All of them, they have the same value. So I can put any power I need during the calculation for any conversion factor. In this case, I need the s square. So I put 2 here.

Then if I rewrite this equation, actually we have m square here times. then one square still is one then we have a square centimeter then 10 to negative 2 square will be 10 negative 4 right now they cancel out and our unit is a square centimeter the answer is equals to 0.951 over 10 negative 4 And again, we can take this to nominator and have 951 times 10 to positive 4. Or, converted to the scientific notation, the answer is 9.51 times 10 to positive 3 square centimeter. In this example, we would like to convert 1.2 liter into cubic feet.

At the beginning, it seems we don't have the conversion factor we need that. But conversion of liter into cubic meter is a very famous conversion factor and everybody needs to know that. 1000 liter is equal to 1 cubic meter. So 1.2 liter times here at the bottom I should have liter so then thousand liter liter and liter they can cancel out and here is one cubic meter. Then we have the information from the question that one meter is equals to 3.28 feet so one meter 3.28 feet.

And here the power for our unit is 3. And here the power is 1. So I need to put the whole conversion factor to the power 3. Then let's rewrite this over 1000 times. Here we have 1 cubic meter. Then feet converts to cubic feet. And 3.28 it should also have a power 3. Then we can have our final answer. 1.2 times 3.28 to power of 3 is equal to 3529 cubic feet and at denominator we have 1000. This 1000. The final answer is equal to 0.042 cubic feet.

And here is the last example. We would like to find out how many years do we have in 6.57 times 10 to positive 6 minutes. So let's write 6.57 times 10 to positive 6 minutes.

So to convert it to the year we need to convert minutes into hour, hour into days. days into years and we know all of these conversion factor so first I'm going to convert minute to hour we know 60 minute is equals to one hour so minutes and minutes they cancel out then the next conversion factor is hours into the day so we know 24 hours is one day then hour and hour they cancel out and then we know each year is 365 days it has a little bit more than that you just simply assume is 365 so 365 day is one year and day and day also they can sell out. so all we have right now is just these numbers 6.57 times to 10 positive 6 here we have 1 1 1 so we don't have anything else for nominator but on denominator we have 60 we have 24 and we have 365. the answer is equals to 12 point five year thank you for watching this video to watch more video please make sure to subscribe to this channel

Transcript for:Unit Conversion & Dimensional Analysis

Transcript for:
Unit Conversion & Dimensional Analysis