I first saw this in chemistry class in College, they called it dimensional analysis and it saved my bacon on many engineering exams. It was fantastic for checking my work to make sure I didn't make some bonehead oversight on an answer.
Another good bacon saver is reality checking the final answer. Had to calc the wire and strand count on a cable lift, damm smashed out the calc in record time, fully lay'd out the workings like dimensional number art and sure as shit looked at my answer so see if it "recons right". Immediately knew I was wrong and found my factor of 10 out in the workings.
Thanks for sharing. I am an engineer also, and as a matter of fact, I thought my kids the exact same thing and it did help them tremendously, often catching by surprise their math or science teachers. One more thing, however, I would like to say is that I also encouraged my kids to doing some mental maths before reaching to the calculator, perhaps to get a feel of the answer beforehand. In your 11 m/s example, I would have encouraged them to convert this to km/h by calculating in their head 11x60x60/1000 = 11x3600/1000 = 11x36/10 = (10x36 + 1x36)/10 = (360 + 36)/10 = 396/10 = 39.6 km/h (I show all the steps to illustrate the process I taught them, but it’s actually quite fast). Then, to quickly convert to mph, I taught them that they can multiply km/h by 0.62, so at this point they are tempted to grab their calculator, but I insist that they “estimate” in their head first so that once they get the answer with the calculator, they’ll know if they punched the right numbers or not depending on the difference with their estimate… So 39.6 x 0.62 should be close to 40 x 0.6 = 4 x 6 = 24. Only at this point, they can grab their calculator to get 24.55 and confidently say that 11 m/s is about 24.6 mph. If you wonder why I teach them the 1 mile = 0.62 km (or its inverse, 1.61), well it is because many cars sold in Canada are fitted with km/h-only speedometers, so when visiting the US, we have to quickly convert back and forth between mph and km/h… therefore 60 mph is a bit less that 100 km/h and so on… So the conversion between inches or feet to cm or metres is not so useful when driving. My two Canadian cents.
YES! Excellent explanation. Understanding this concept and putting in the work to make it second nature was one of the fundamental keys for my surviving engineering school all those years ago. I remember getting the dopamine hit from doing it successfully -- so satisfying! I remember there being a ton of it on the EIT exam as well. Somehow dimensional analysis clicked for me early on, and I was grateful for that. Thanks for sharing!
I was luck when studying doing structural analysis I aced many tests and exames and that Dopamine kick in and yes it was very gratifying knowing you did it perfect. I remember the look of my professors face when he gave me my tests and exams . It was Priceless...lol
This was very useful! I'm a mechanical engineering student. I find as a mature student stuff like this is assumed to be known and skipped over to a certain degree. I'll make a point of practicing this!
I teach chemistry at the college level. This strategy is called factor-label method. The dimensional analysis is going through the units and making sure all the units not needed are cancelled out in the process and only the units you are looking for are left to be applied to the numerical answer (cancelling the units). I teach a chemistry for engineering students course here in Texas meant to show the engineering students what they need for their engineering careers without making them take the two traditional courses. I show them the fraction aspect from a mathematics view point but I will share this video to help them see it from the engineers stand point and your video emphasizes the importance of the method for engineers (in their courses and careers).
I remember my first year in engineering school, I have this mechanics of materials teacher that always does their problem solving with this dimensional analysis, at first I wasn't getting what he was doing in that black magic witchery but after having a good think at that I just got that click that it was just like making multiplications by 1 but getting advantage of the units equivalence, thanks to all the teachers that solves problems step by step not assuming that everyone knows just how to do it in first years of school.
Wow... Interesting thing, I think I never learned that on school. On the other hand you really made the point why people used to the metric system can't understand why the US system is still in use 😀
I wish we had learned useful stuff like this in highschool; math was my enemy, but now I use it daily as a hobby engineer and end up struggling through stuff like this and seeing the value of it because now, 20 years later, I finally have a use for it!
This reminds me of Nuke school in the Navy, I had seen the principles before in HS chemistry but in Nuke school it was referred to as ladder analysis where a line was separated into boxes units filled in and result at the end. Thanks for the entertaining video and memories.
I was taught this in my pre-calc class in highschool. multiply by 1 and dont divide by zero. But similarly the light did not go on till eng school, even then i did not upload units conversion was still multiplying by one till much later. I am teaching my kids now starting with fractions.
This is an awesome explanation of dimensional analysis! I've gotten pretty quick with it at this point in engineering school, but this is definitely a super important skill to refine, and I appreciate that you make resources like this to explain some of these key concepts. Coming from a sophomore aerospace engineering student, we use this sort of thing a lot to the point where its become second nature to me.
As a Brit, we still measure distance on the road in miles, but for just about everything else now we use the metric system. I watched scrapheap/junkyard challenge in the past with teams from the US and the amount of torture you put yourselves through jumping units and systems is mind blowing!!!
We were never taught this, but it always just seemed intuitive (or obvious or however that phrase should work). Given the comments, I think then I've been very lucky to have understood this very early on
When I learned this in High School, we called in "Ninja Math". Not sure where the term came from, possibly from the slashing motion of canceling common terms :)
Oh, I was only 1/4th into the video when I commented this. It is called dimensional analysis, and in chemistry you are often working specifically to find stoichiometric ratios/quantities, called stoichiometry dimensional analysis, often shortened to just stoichiometry. This is what I do in any physics/engineering class right now, so glad I was acquainted with it in high-school!
Thanks! That's what I remember from high school chemistry, working the stoichiometry. The teacher just kept repeating examples and I wasn't getting it (but I also wasn't very interested in chemistry). Once I got to physics with calculus suddenly everything made sense!
@@BUILD2 same-physics. Just reasoning, thinking through the relations I knew and the data I had. Then check the dimensions and evaluate the integral. Guess what? It’s going to work out correct 9 times out 10 if you have sane dimensions in the end. Otherwise who knows?
Useful trick is to use Google search. You can ask it f.e., "30 gallons per mile in teaspoons per lightyear". I use their converter a lot when I'm trying to do quick calculations.
Imperial system is so unintuitive for EVERYTHING! It makes no sense! What are the relations among feet, inches, yard, mile and whatever made up unit you come along? Metric system uses the same multiplier/divider for everything: you have a meter... want 1000th of it? Simple! Use mili: mili-meter. Wants 10 times it? Simple! Use deca: deca-meter. Want 1/10th of 1000 times a Newton? Simple! 1000/10 = 100 = hecto -> hecto-Newton! Want to do the same thing for lumens? No problem! Hecto-lumen!!! Want one millionth of a Farad? Great: 1 microfarad!!!
Oh do I feel ya on that one thing tgat turned the tide. As in: Even though I tutored with my Alg1 teacher, she only lived 5 houses away, she still failed me bec of an order of operations process that wasn't clear to me. Within 10mins of Dumber sch, another math teacher gave me a most simple mnemonic to get me to see over the boulder. And I passed Geo & Trig in the following 2yrs. Bec The Library of Alexandria is literally at our fingertips, keep adding to the World's Encyclopedia, The Net
You won’t believe but I failed my first quiz on converting units. Now that I reflect about that, I feel ridiculous hahaha but I guess one must fall to get up stronger. Thanks for sharing ur knowledge with the world.
Btw, would love to see something on how tools like differential equations are used to compute driving limit issues that involve road conditions, slip angles, & speed, wrt "acceptable/comfortable" ranges of cornering & acceleration/deceleration forces!
This was first explained to me in high school chemistry. I don't remember it ever having a name, however a few years down the road I have heard it referred to as factor/ label.
I've never seen this done before. It just seems more intuitive to me to multiply/divide by whatever ratio needed to skip from unit to unit. Like I would just multiply 11 by 3600 and divide by 1000 ... or rather just multiply by 3.6 right away. This does seem like a good way to teach it, though, for students who have a hard time combining the ratios as they skip from unit to unit. I didn't bother with the cm/inch step either as I just fudged a value of 1.61 km/mile. Close enough!
I felt the same way when I was first started my engineering degree. However, I found some conversions used units I wasn't familiar with (ex. horse power to kilowatts) or took a number of conversions to get to the final answer. Once I mastered this though I new I could confidently convert with out questioning myself and I had the work to prove it and double check with. But yah after doing a specific conversion over and over you start to the hang of doing it in your head, or just rattle it off on a calculator. I still find my self making mistakes though. One thing I learned from my degree is having a record of your work and every justification for the work that you did is invaluable!
I grew up in "metricland" and I'v done all the math a long time a go.. now I just remember a few conversion numbers. Mi - km =1.6 cm - inch = 2.54 m/s - km/h = 3.6 (also Kbyte/sec - Mbyte/H = 3.6) or 4" = 10cm (40" = 1m) 30mph = 50km/h 50mph=80km/h and from those I can calculate almost anything without the use of a calculator , these number are not exact but wil do for daily use. for some reason we stil use thumbs (inches) for inside diameter of tubes.....
I'm a year away from graduation and I never see this kinda stuff. All I see is Fourier Transforms, Root Locus, Maxwell's Eq... I wish it were like this.
There's ~1609 m in a mile or as I was thought 1600m = 1 mile. The worst one I had was instead of an acceleration value in m/s2 I got told in "Gravities" that was horrible, completely threw me at first.
Can anyone guess which trick scientists like weathermen and theoretical scientists are using The most? Also if u r owning banks and I guess finance in generally these days.. Lol. Its Kinda magically actually
For some reason it keeps bothering me that you cut the pizza twice without stopping at 2/4+4/8=1. Kid in class: "Am I ever going to actually use all this algebra?" Math teacher: "You won't, but one of the smart kids might."
I learned this concept in second grade. I never really thought bout it, but after seeing you explain it, its is even clearer to me now. Thanks for the different prospective.
Nein, aber meine Frau und ich haben Deutsch zusammen studiert and viele mal Deustchland besichtigt. Auch gibt es Deustche Stammtische hier in den USA. Gestern habe ich ein Podcast "MDR KULTUR-Cafe'" gehoert. Es verbessert meine verstaendnis! I'm sure I made a bunch of mistakes typing that but have really enjoyed visiting the smaller towns in Germany where Americans almost never go. It's cheaper and prettier than the bigger towns and leads to experiences I will never forget!
@@BUILD2 Dein (ihr) Deutsch ist besser als das mancher einheimischen. Waren sie auch in der Nähe von Hamburg? Dort gibt es sehr viele schöne kleine Dörfchen. I didn't know that the German language was still spoken in America, I thought it went extinced after WWII.
@@BUILD2 I thought you studied engeneering, I also want to study Maschinenbau (mechanical engineering) and love the technical side of your videos. I learned so much already. Thank you
I first saw this in chemistry class in College, they called it dimensional analysis and it saved my bacon on many engineering exams. It was fantastic for checking my work to make sure I didn't make some bonehead oversight on an answer.
Another good bacon saver is reality checking the final answer. Had to calc the wire and strand count on a cable lift, damm smashed out the calc in record time, fully lay'd out the workings like dimensional number art and sure as shit looked at my answer so see if it "recons right". Immediately knew I was wrong and found my factor of 10 out in the workings.
Thanks for sharing. I am an engineer also, and as a matter of fact, I thought my kids the exact same thing and it did help them tremendously, often catching by surprise their math or science teachers. One more thing, however, I would like to say is that I also encouraged my kids to doing some mental maths before reaching to the calculator, perhaps to get a feel of the answer beforehand. In your 11 m/s example, I would have encouraged them to convert this to km/h by calculating in their head 11x60x60/1000 = 11x3600/1000 = 11x36/10 = (10x36 + 1x36)/10 = (360 + 36)/10 = 396/10 = 39.6 km/h (I show all the steps to illustrate the process I taught them, but it’s actually quite fast). Then, to quickly convert to mph, I taught them that they can multiply km/h by 0.62, so at this point they are tempted to grab their calculator, but I insist that they “estimate” in their head first so that once they get the answer with the calculator, they’ll know if they punched the right numbers or not depending on the difference with their estimate… So 39.6 x 0.62 should be close to 40 x 0.6 = 4 x 6 = 24. Only at this point, they can grab their calculator to get 24.55 and confidently say that 11 m/s is about 24.6 mph. If you wonder why I teach them the 1 mile = 0.62 km (or its inverse, 1.61), well it is because many cars sold in Canada are fitted with km/h-only speedometers, so when visiting the US, we have to quickly convert back and forth between mph and km/h… therefore 60 mph is a bit less that 100 km/h and so on… So the conversion between inches or feet to cm or metres is not so useful when driving. My two Canadian cents.
YES! Excellent explanation. Understanding this concept and putting in the work to make it second nature was one of the fundamental keys for my surviving engineering school all those years ago. I remember getting the dopamine hit from doing it successfully -- so satisfying! I remember there being a ton of it on the EIT exam as well. Somehow dimensional analysis clicked for me early on, and I was grateful for that.
Thanks for sharing!
I was luck when studying doing structural analysis I aced many tests and exames and that Dopamine kick in and yes it was very gratifying knowing you did it perfect. I remember the look of my professors face when he gave me my tests and exams . It was Priceless...lol
This was very useful! I'm a mechanical engineering student. I find as a mature student stuff like this is assumed to be known and skipped over to a certain degree. I'll make a point of practicing this!
Awesome. You and your classmates are the intended audience!!!
I teach chemistry at the college level. This strategy is called factor-label method. The dimensional analysis is going through the units and making sure all the units not needed are cancelled out in the process and only the units you are looking for are left to be applied to the numerical answer (cancelling the units). I teach a chemistry for engineering students course here in Texas meant to show the engineering students what they need for their engineering careers without making them take the two traditional courses. I show them the fraction aspect from a mathematics view point but I will share this video to help them see it from the engineers stand point and your video emphasizes the importance of the method for engineers (in their courses and careers).
I thought I've mastered this and yet today I was converting something and I had to open this video to refresh my understanding! thanks.
Wonderful!
I remember my first year in engineering school, I have this mechanics of materials teacher that always does their problem solving with this dimensional analysis, at first I wasn't getting what he was doing in that black magic witchery but after having a good think at that I just got that click that it was just like making multiplications by 1 but getting advantage of the units equivalence, thanks to all the teachers that solves problems step by step not assuming that everyone knows just how to do it in first years of school.
Wow... Interesting thing, I think I never learned that on school.
On the other hand you really made the point why people used to the metric system can't understand why the US system is still in use 😀
More math videos on UA-cam can only be a good thing. Thanks for posting this!
I wish we had learned useful stuff like this in highschool; math was my enemy, but now I use it daily as a hobby engineer and end up struggling through stuff like this and seeing the value of it because now, 20 years later, I finally have a use for it!
This reminds me of Nuke school in the Navy, I had seen the principles before in HS chemistry but in Nuke school it was referred to as ladder analysis where a line was separated into boxes units filled in and result at the end. Thanks for the entertaining video and memories.
I was taught this in my pre-calc class in highschool. multiply by 1 and dont divide by zero. But similarly the light did not go on till eng school, even then i did not upload units conversion was still multiplying by one till much later. I am teaching my kids now starting with fractions.
This is an awesome explanation of dimensional analysis! I've gotten pretty quick with it at this point in engineering school, but this is definitely a super important skill to refine, and I appreciate that you make resources like this to explain some of these key concepts.
Coming from a sophomore aerospace engineering student, we use this sort of thing a lot to the point where its become second nature to me.
As a Brit, we still measure distance on the road in miles, but for just about everything else now we use the metric system. I watched scrapheap/junkyard challenge in the past with teams from the US and the amount of torture you put yourselves through jumping units and systems is mind blowing!!!
Barney Barret, if you guys got along with the French and hadn't sponsored pirates to annoy their trade businesses, very likely we would be metric lol.
Who knew you could just cancel the unit labels like that! I remember seeing that somewhere and being taken aback for a second. Great refresher.
I'm about a year away from graduating as a robotics engineer and yeah, i can confirm we use these the most
Not Laplace transforms?
What school because I am also close to graduation and I never see this kinda stuff.
I'm studying electrical engineer (I'm paraguayan) and we also use to flip to imperial lol
We were never taught this, but it always just seemed intuitive (or obvious or however that phrase should work). Given the comments, I think then I've been very lucky to have understood this very early on
When I learned this in High School, we called in "Ninja Math". Not sure where the term came from, possibly from the slashing motion of canceling common terms :)
Nice! I may adopt that!
Ode to Dimensional Analysis! :)
Oh, I was only 1/4th into the video when I commented this. It is called dimensional analysis, and in chemistry you are often working specifically to find stoichiometric ratios/quantities, called stoichiometry dimensional analysis, often shortened to just stoichiometry. This is what I do in any physics/engineering class right now, so glad I was acquainted with it in high-school!
Thanks! That's what I remember from high school chemistry, working the stoichiometry. The teacher just kept repeating examples and I wasn't getting it (but I also wasn't very interested in chemistry). Once I got to physics with calculus suddenly everything made sense!
@@BUILD2 same-physics. Just reasoning, thinking through the relations I knew and the data I had. Then check the dimensions and evaluate the integral. Guess what? It’s going to work out correct 9 times out 10 if you have sane dimensions in the end. Otherwise who knows?
Your chem teacher should have done calculus so it would have made sense.
Useful trick is to use Google search. You can ask it f.e., "30 gallons per mile in teaspoons per lightyear". I use their converter a lot when I'm trying to do quick calculations.
I love that I've grown up with the metric system. Imperial is so unintuitive for doing equations.
Metric system.... let’s see you cut a pizza into 10 equal pieces, then tell me how great that metric system is.
@@aqueousone What do you want to say? Fractions are still a thing in the metric system.
@@aqueousone cut in 12 equal pieces, then tell me how great that imperial system is. Or in 5280 / 25.4 x 12 x ........... oh hell!
Imperial system is so unintuitive for EVERYTHING! It makes no sense! What are the relations among feet, inches, yard, mile and whatever made up unit you come along?
Metric system uses the same multiplier/divider for everything: you have a meter... want 1000th of it? Simple! Use mili: mili-meter. Wants 10 times it? Simple! Use deca: deca-meter. Want 1/10th of 1000 times a Newton? Simple! 1000/10 = 100 = hecto -> hecto-Newton! Want to do the same thing for lumens? No problem! Hecto-lumen!!! Want one millionth of a Farad? Great: 1 microfarad!!!
@@danielkohwalter5481 The lack of intuitiveness is why we like it : ) Why make it easy when you can make it interesting!
Oh do I feel ya on that one thing tgat turned the tide. As in: Even though I tutored with my Alg1 teacher, she only lived 5 houses away, she still failed me bec of an order of operations process that wasn't clear to me. Within 10mins of Dumber sch, another math teacher gave me a most simple mnemonic to get me to see over the boulder. And I passed Geo & Trig in the following 2yrs.
Bec The Library of Alexandria is literally at our fingertips, keep adding to the World's Encyclopedia, The Net
You won’t believe but I failed my first quiz on converting units. Now that I reflect about that, I feel ridiculous hahaha but I guess one must fall to get up stronger. Thanks for sharing ur knowledge with the world.
Btw, would love to see something on how tools like differential equations are used to compute driving limit issues that involve road conditions, slip angles, & speed, wrt "acceptable/comfortable" ranges of cornering & acceleration/deceleration forces!
This was first explained to me in high school chemistry. I don't remember it ever having a name, however a few years down the road I have heard it referred to as factor/ label.
Jup, also an engineer here and I also use this all the time.
I've never seen this done before. It just seems more intuitive to me to multiply/divide by whatever ratio needed to skip from unit to unit. Like I would just multiply 11 by 3600 and divide by 1000 ... or rather just multiply by 3.6 right away. This does seem like a good way to teach it, though, for students who have a hard time combining the ratios as they skip from unit to unit. I didn't bother with the cm/inch step either as I just fudged a value of 1.61 km/mile. Close enough!
I felt the same way when I was first started my engineering degree. However, I found some conversions used units I wasn't familiar with (ex. horse power to kilowatts) or took a number of conversions to get to the final answer. Once I mastered this though I new I could confidently convert with out questioning myself and I had the work to prove it and double check with. But yah after doing a specific conversion over and over you start to the hang of doing it in your head, or just rattle it off on a calculator. I still find my self making mistakes though. One thing I learned from my degree is having a record of your work and every justification for the work that you did is invaluable!
I’m taking a guess,
Is it dimensional analysis?
Update
Yep totally correct, a must have in the engineering world.
I grew up in "metricland" and I'v done all the math a long time a go.. now I just remember a few conversion numbers. Mi - km =1.6 cm - inch = 2.54 m/s - km/h = 3.6 (also Kbyte/sec - Mbyte/H = 3.6) or 4" = 10cm (40" = 1m) 30mph = 50km/h 50mph=80km/h and from those I can calculate almost anything without the use of a calculator , these number are not exact but wil do for daily use. for some reason we stil use thumbs (inches) for inside diameter of tubes.....
My careers adviser at school showed me this formula: cant spell + good at math = engineer
That's why a Mathcad window is always open on my desk top.
I'm a year away from graduation and I never see this kinda stuff. All I see is Fourier Transforms, Root Locus, Maxwell's Eq... I wish it were like this.
You wish all math was dimensional analysis? Lol
Im so happy i didnt have to know 5280 and stuf😂😂
i can relate. love the metric
But, what if you make 4 pieces from upper half and 2 pieces from lower half? That is not going to be equals to 1.
There's ~1609 m in a mile or as I was thought 1600m = 1 mile. The worst one I had was instead of an acceleration value in m/s2 I got told in "Gravities" that was horrible, completely threw me at first.
Works for currency conversion as well.
It's not delivery, it's Digiorno.
Also, 9:06, I too as an american keep wanting to say a unit in german instead of english.
I was taught it in high school as dimensional analysis
The next step is to convert everything to SI base units (kg, m, s etc.) at the start. Then you don't have to care for units at all
Keep it up
Can anyone guess which trick scientists like weathermen and theoretical scientists are using The most? Also if u r owning banks and I guess finance in generally these days.. Lol. Its Kinda magically actually
Spill the beans man
For some reason it keeps bothering me that you cut the pizza twice without stopping at 2/4+4/8=1.
Kid in class: "Am I ever going to actually use all this algebra?" Math teacher: "You won't, but one of the smart kids might."
I'm in the UK and we use ft and inches also miles MPH
Really? Good to know! I've been to Europe many times but never the UK.
We use both metric and imperial in the UK. Jack of all master of none :D
Yeah well, guess which "empire" the imperial system comes from ;)
you should be a Professor at University
Have you lived in Germany?
Nee, aber oft besucht. :)
I learned this concept in second grade. I never really thought bout it, but after seeing you explain it, its is even clearer to me now. Thanks for the different prospective.
I am familiar with the speed of smell
Merica!!!
Why do you want to say it in German?
If you can speak German I would love to her your German voice. Hast du in Deutschland studiert?
Nein, aber meine Frau und ich haben Deutsch zusammen studiert and viele mal Deustchland besichtigt. Auch gibt es Deustche Stammtische hier in den USA. Gestern habe ich ein Podcast "MDR KULTUR-Cafe'" gehoert. Es verbessert meine verstaendnis! I'm sure I made a bunch of mistakes typing that but have really enjoyed visiting the smaller towns in Germany where Americans almost never go. It's cheaper and prettier than the bigger towns and leads to experiences I will never forget!
@@BUILD2 Dein (ihr) Deutsch ist besser als das mancher einheimischen. Waren sie auch in der Nähe von Hamburg? Dort gibt es sehr viele schöne kleine Dörfchen. I didn't know that the German language was still spoken in America, I thought it went extinced after WWII.
@@BUILD2 I thought you studied engeneering, I also want to study Maschinenbau (mechanical engineering) and love the technical side of your videos. I learned so much already. Thank you
Poor Pizza
Vive la HP 48G