[Music] hi i'm rob welcome to math antics in this lesson it's finally time for us to learn about time like distance time is something you can measure and represent as a number but we use different units to measure time and also different devices to make the measurements there are lots of different units of time from really small ones like nanoseconds to really big ones like centuries but in this video we're only going to learn about four of the most common units of time seconds minutes hours and days you should be really familiar with a day you know because you encounter one every day a day is the amount of time it takes the earth to rotate on its axis one time so it's pretty much the fundamental unit of time for our planet but as important as a day is we need smaller units of time for planning daily activities so people decided to divide up each day into 24 equal chunks of time called hours even though an hour is only 1 24th of a day it's still a pretty long time so we divide hours up into even smaller units called minutes specifically each hour is divided up into 60 minutes so a minute is 1 60 of an hour and to get even smaller units of time we divide up each minute into 60 equal parts called seconds so a second is 1 60 of a minute going from the smallest to the biggest you should memorize that 60 seconds equals 1 minute 60 minutes equals 1 hour and 24 hours equals one full day there are some common abbreviations for these units that you should know too d for days h for hours min for minutes and s for seconds one of the earliest devices for measuring time was called a sundial it was basically a flat disc with a triangular pointer in the middle as the earth rotated the shadow of the pointer would slowly change position and point to different markings on the edge of the circle which represented different times of the day are you tired of the man telling you what time it is now you can get the time directly from the source with the sunomatic 3000 just put it in your yard and let the sun do the rest for daytime use only not for use in cloudy conditions times may not be accurate depending on latitude some calibration required the sundial was a really cool invention but it had a lot of limitations fortunately there are much better modern devices for keeping track of time in fact you probably have one hanging on your wall at home or in your classroom that looks something like this this traditional clock is designed to keep track of three different units of time seconds minutes and hours that's why it has three different pointers or hands this thin red pointer is called the second hand because it helps us keep track of seconds this thicker black pointer is called the minute hand because it helps us keep track of minutes and this shorter black pointer is called the hour hand because it helps us keep track of hours oh and the circle itself is often referred to as the clock face a clock is actually kind of complicated so to see how it works let's start with the version that has everything removed except for the second hand and the 60 marks around the edge of the clock face why are there 60 marks around the edge you'll see in just a minute starting with the second hand pointing straight up at the top of the clock face if the hand rotates to the right so that it's pointing at the next mark that means that one second of time is passed so we'll label that mark one the next mark will be two the next three and so on until we get all the way around and the hand is pointing straight up again that means exactly 60 seconds have passed so label that mark with a 60. but we could have labeled that top mark as a zero since that's where the sequence of numbers starts that's one of the cool things about a clock being a circle the starting point is also the ending point so as soon as you hit the end 60 seconds you're also back at the beginning zero seconds the reason that there's exactly 60 marks around the edge of a clock is that 60 seconds equals one minute that means when the second hand makes one full rotation around the clock face exactly one minute of time is passed and if it makes two full rotations two minutes have passed and if it makes three rotations three minutes have passed and so on so even though the second hand is counting seconds it also helps us know how many minutes have passed but how are we going to keep track of those minutes well that's where the minute hand comes in handy so let's add it back to our simple clock the minute hand works a lot like the second hand the main difference is that it travels slower 60 times slower to be exact since a minute is 60 times longer than a second while the second hand travels all the way around the clock the minute hand only moves from one mark to the next for example if both hands start straight up at the top of the clock while the second hand travels all the way around the clock counting out 60 seconds as it goes the minute hand will only travel from zero to one because only one minute has passed then while the second hand travels around the clock a second time the minute hand will travel from one to two because 2 minutes have passed notice that we use the exact same set of 60 marks to measure both seconds and minutes but the different hands tell you how to interpret those marks if the second hand is pointing at the 5th mark it means five seconds but if the minute hand is pointing at the fifth mark it means five minutes of course being able to quickly tell which mark a hand is pointing at is tricky since clocks don't usually number every mark so to make it easier the inventors of the clock decided to make every fifth mark bigger or bolder so you could skip count by fives which helps you quickly tell where the hands are pointing for example if the second hand is pointing right here you can tell right away that it's just two marks past the 15th mark so it's pointing at 17 seconds since 15 plus 2 equals 17. and if the minute hand is pointing here you'll quickly see that it's just two marks before the 40th mark so it's pointing to 38 minutes since 40 minus 2 equals 38. these bigger marks are so helpful for reading a clock that you should memorize the values they represent when the minute or second hands are pointing at them especially the ones that break the clock face up into quarters okay so now you know how the second and minute hands work when the second hand goes all the way around the minute hand increases by one but what happens when the minute hand eventually goes all the way around and is counted out 60 minutes if you paid close attention at the beginning of the video you probably know the answer 60 minutes equals one hour so when the minute hand goes all the way around it means one hour of time is passed that means we're going to need to add the hour hand back to our clock to keep track of hours but the hour hand doesn't use the 60 marks on the edge of the clock in the same way that the other hands do why not because there aren't 60 hours in a day there's only 24. if the hour hand just moved one mark for each hour it wouldn't make it all the way around the clock face in a single day ideally it would be nice if we could have the hour hand go around the clock once per day but unfortunately the 60 marks on the clock don't divide evenly by 24. that means you can't find a nice whole number to skip count to 24 by for example if you had the hour hand move two marks for each hour it still wouldn't go far enough to make it all the way around the clock in a day and if you had it move three marks for each hour it would go too far fortunately the inventors of the clock came up with a clever compromise they realized that even though 24 hours doesn't divide evenly into 60 half of a day which is 12 hours does 60 divided by 12 equals 5 and 5 is a nice whole number to skip count by in fact we already have bigger marks on our clock face every 5 marks which makes this idea really convenient if the hour and minute hands start pointing straight up as the minute hand goes all the way around the clock counting out 60 minutes the hour hand will slowly move past the first five marks which means one hour has passed then as the minute hand goes all the way around again the hour hand will move past the next five marks which means that two hours will have passed this continues on until the hour hand makes it all the way around the clock and gets to the 12 hour mark back at the top just like with minutes and seconds the top position on the clock represents both the beginning and the end of the counting sequence for minutes and seconds that means the top position represents both 60 and zero but for the hour hand that top spot represents both 12 and zero of course 12 hours is only half a day that means in order for this clock to keep track of one whole day the hour hand needs to make two full trips around the clock face it counts out 12 hours the first half and then 12 more for the second half that means that each hour mark is passed twice during the day so we need a way to distinguish them and that's where am and pm can help us out am stands for anti-meridian which just means before noon and pm stands for post meridian which just means afternoon to see how the am and pm labels work with the 12 hours on our clock face to keep track of a full day let's compare them to a simpler modern time keeping system called the 24 hour clock in that system the 24 hours of the day are just labeled 0-23 in other words at the beginning of the day which happens to be midnight the time is 0 hours and 0 minutes as the hours pass by you eventually get to the time 23 hours and 0 minutes which means you're starting the 24th hour of the day after that last hour passes it starts back over at zero for the next day on the traditional clock face at midnight the hour hand is pointing straight up at 12 so instead of calling it zero o'clock we call it 12 midnight or 12 am then the first 12 hours of the day pass one by one using the am label 1 am 2 am 3 am on up to 11 am when the hour hand gets to 11 am you're beginning the 12th hour of the day and as soon as the 60 minutes of that hour pass by the hour hand will be back up at the top of the clock pointing at 12 again but this time we're going to call that position 12 noon or 12 p.m then the clock continues on counting out the last 12 hours of the day using the pm label 1pm 2 pm 3 pm on up to 11 pm when the hour hand gets to 11 pm it means you're starting the last or 24th hour of the day after that last hour passes the hour hand points straight up at 12 again which is now 12 midnight or 12 am and the cycle starts all over for the next day let's briefly summarize what we've learned about the clock so far before moving on to a few examples of telling time each time the second hand rotates all the way around the clock one minute has passed and the minute hand advances one mark each time the minute hand goes all the way around the clock one hour has passed and the hour hand advances five marks each time the hour hand goes around the clock 12 hours have passed which is half a day the first 12 hours are called the am hours and the second 12 hours are called the pm hours if this is your first time learning how a clock works it might seem kind of confusing but don't worry the more you practice looking at a clock and noticing which hands are pointing to which marks the faster you'll be able to tell what time it is in fact let's practice that a few times now so you can get the hang of it before doing more practice on your own let's start with this clock face what time of day is it displaying the hour hand is past the seven but not to eight yet so the hour is seven the minute hand is pointing directly at the three but remember that's the third group of five marks for counting minutes or seconds so it's pointing at the 15 minute mark and the second hand is pointing straight up which is the zero second mark so the time is seven hours 15 minutes and zero seconds oh and that's how you write time using numbers you write the hours first then minutes and then seconds if necessary all separated by colons but is this 7 15 am or pm to tell that you need to know if it's before noon or afternoon the halfway point of the day books or tests sometimes give you a clue about whether the time is before noon or afternoon so you can figure it out or they may just tell you if it's am or pm in this case we're given the clue soon the sun will set so we know it's afternoon or 7 15 pm how about this example what time is this clock displaying the hour hand is past the 10 but not to 11 yet so the hour is 10. the minute hand is just past the 4 which is the 20 minute mark but it's not to 21 yet so the minute is 20 and the second hand is pointing at the 9 which is the 45 second mark so the time is 10 hours 20 minutes and 45 seconds and this time you're given the clue it's a beautiful morning so you know that it's 10 20 am since morning comes before noon and finally what time of day is this clock display the hour hand is past the 12 but not yet to the one so it's 12 something the minute hand is pointing just a hair past the six which is the 30 minute mark so the minute is 30. and there's no second hand on this clock not all clocks have them so we're only concerned about the time to the nearest minute in this example lastly this clock face is actually labeled am so we know that the time of day is 12 30 a.m which is 30 minutes past midnight all right so now you know how seconds minutes hours and days all relate to each other you also know how a traditional clock works to help you keep track of these units of time as they pass by and importantly you've learned how to read the hands of the clock face so that you can tell what time of day it is remember that the way to get good at anything in math is to practice so be sure to practice telling time on your own as always thanks for watching math antics and i'll see you next time learn more at mathantics.com