 Greetings and welcome to Math Help for Science Courses. In this lecture we are going to go through and talk about some of the different types of scientific calculators that are around and how to go about using those. So let's look at an example of one scientific calculator. And here is one that many of you may have seen before, a standard Texas Instruments calculator. And it works, a scientific calculator has more functions than a general calculator. An ordinary calculator has basic functions like addition, subtraction, multiplication, and division, which are also present on a scientific calculator. Sometimes a traditional calculator will have a square root key or some other basic functions. But what you note here is that there's a lot of other functions here, we have the trigonometric functions that we may use, we have different ways to do exponents here, here, and here. So we have a number of different ways and we also have logarithms here. So there's some other things that we may use in various science courses. Now there are traditional calculators which would be the example that we see here. However, there are also other calculators that you can use. If you don't have a scientific calculator, unless your instructor requires you to have one, you can often use an online calculator. And here is one example of that. And that is the website given here is web2.oCalc.com. So you can go there to see a free online calculator that you can use. And as we see with a traditional calculator, it does have the basic functions, addition, subtraction, multiplication, and division. And it also has a number of the other functions here, primarily those related to the trigonometric functions over here. Different values, different ways of doing exponents here, and again the logarithm is down here. So there are more and more functions as you get to more complicated calculators. But again, all of the same functions that you might use are here. And we can also look at the other things that people use. We had the traditional calculators we looked at, we had online calculators. You can also, most people now with a smartphone will also have calculators that are built in there. And here is an example of the scientific calculator built in to the iPhones. So you can use this. There are also a number of free apps that you can download for both Apple and Android devices that you can download that will also have similar functions. But this is one. And on the iPhone, for example, if you use your phone in the portrait mode holding it straight up and down, it will just give you the basic functions. It will only have essentially mostly the stuff over here. You can add, subtract, multiply, and divide. However, if you turn it sideways into landscape mode, then it actually turns into a scientific calculator. And you can then access, as we've looked at before, various trigonometric functions, various different ways to do exponents here, and different parts of logarithms over here. So those are all present. Now, for most science courses, you will need these. You will need to be able to enter numbers in these, be able to raise numbers to various powers or take various roots, and to use some of the trigonometric functions. And occasionally in courses, you may even use logarithms. Another one that you'll often use is the double E button here, which is the button for scientific notation. So when able to put the number into scientific notation, you would then press the number you want, and then the double E key, and then the power of 10. So for 5 times 10 to the second power, you would write that as, put that in as the 5. You'd press the double E key, and then press 2, and that would enter the same number. And what you will find is that equals 500, and your calculator will automatically convert that. If it's a small enough number, it will automatically do that conversion. Now, we've looked at a couple of different types of calculators here, and what you want to remember is that each of these is different. So there are some differences in how things are set up on these calculators, how they go about looking at various things. So we have, they're in different positions. So if we look at how things are set up on the iPhone calculator here, the trig functions are down at the bottom, and the exponentiation functions are up above them. However, on a Web 2.0 calc that I mentioned, it's done differently where the trigonometric functions are to the left, and then the exponentiations are in between. So how they're set up may be different, how they're used can be different as well. So in each of them, you can have a little bit different settings, and in the TI calculator, again, things are all a little bit different in terms of how things are set up. So let's look at some of the uses, and for this I'm going to use the Web 2.0 calculator that you want to look at, and one of the ways to use, one of the things we can do with that is that, of course, it's accessible to everybody. It's one that anyone can access because it doesn't require that you have a specific type of calculator or a specific type of phone, you can simply go to the Web site and use this scientific calculator. So what do we have on these? We have the basic math functions which are over here, addition, subtraction, multiplication, and division. So you can do those exactly the same. Powers and roots. So if we want to square a number, we can just put the number in and then press the X squared button, and that will give us the square. So if you put 5 in and press the X squared button, then you would get 25. If you want to do a square root, you can do the same thing, put in 25, press the square root button, and get the number 5 out. So those are some of the things that you can do. You can also do third powers and third roots, but in some cases you may need to do different powers. What if you wanted to find, for example, 5 to the 2.5 power? Well, there is no 2.5 button in there. What you'd use is this X to the Y. So you would put in the 5, then you would press the X to the Y button, and then you would press 2.5, and that would then take 5 and raise it to the 2.5 power. So you can do that. You can also do roots the same way. If you want to raise things to take the 2.5 root of something, you would push that key instead. So there are various ways to be able to do that, and sometimes in a calculation you'd need that. We use sometimes the trigonometric functions in various classes. Primarily sine, cosine, and tangent would be the most often used here. Others would be very rarely used in most basic science classes, but you may see situations to use these, or they're inverses. Now inverses can be accessed by pressing usually a second key. On some calculators it might be the inverse key. So there are various different things that you might have to push there, but that will then access and turn these into their inverse, turn the trigonometric functions into their inverse functions. So what you would see is if we were to push that second button, you would see this, and if you note how things have changed, a lot of it stayed exactly the same. We didn't have anything that changed here. The powers are still exactly the same. The logarithms are still exactly the same. But these have changed from sine to asine. So, and cosine, cos to a cosine. So they now are doing the inverses. And there are some cases where you need that function. You just have to push that second button, or sometimes the inverse button first. Now in some cases it will lock. In other cases it will not. And again you're going to have to experiment with it and discuss with your instructor the exact details of the specific calculator that you are using. There are also various constants that are embedded into these. You have the constant button here. And you will find when you start out, if we go back, that originally that shows the pi, which would be the most often used constant. However, if you have the second function enabled and you push that and then you would see this as the constant button. And if you actually push that on Web 2.0 calc, it will come up with a menu that will have dozens and dozens of different constants that may be used in various scientific situations. You can use that of course. You can also enter the numbers manually as well. Now one of the more important things that we do use here is to have numbers in scientific notation. So we want to be able to enter numbers in scientific notation and this again does vary depending on the type of the calculator that you use. I showed you an example previously of how to do this on the iPhone calculator using the double E button to enter it. You can also use the EXP button on some calculators which will do the same thing. So again, 5 times 10 to the second, you would do 5 double E2 on the iPhone calculator. You might do 5 EXP2. Again, these are the buttons that you would push on other calculators that have an EXP button. How about for the Web 2.0 calc button? Well, let's look at how we would do that. Well, in this case you would use the E button. If you look at this little E up here, it is used then for the scientific notation button. And you have to be very careful with what you use when you're trying to enter numbers in scientific notation. It's often wanted to use the 10 to the X key here and just to multiply. So what you often people want to do is write 2.5 times, hit multiplication, and then 10 to the third power, for example. That does not work out well because it will cause problems with the correct order of operations. It sees that, and if we have a number as 2.5 times 10 to the third, it sees that as 2 numbers, so you're multiplying. Then if we try to divide that by another scientific notation, or take, you know, 15 divided by this, it will divide it by the first number and then multiply it by the second, which is not correct. In this case you would have to put this in parentheses. So let me show you the easier way to do that here, and that is using the E key. And you use that just like you use the double E key on the iPhone or the EXP key on other calculators. And all you have to do is if you want to write a number, you would write 2.5, press the E key, and then you're exponent. And that would automatically do the calculation in the scientific notation, and it will look at that as a single number. So you don't have to worry about keeping track of all the extra parentheses you would need if you wanted to use the multiplication key. So I strongly discourage using the multiplication key when entering scientific notation. It's not the way it's supposed to be done. So let's finish up here with a little bit of what we've covered. First of all, we talked about there are a wide variety of scientific calculators. They're all different. And you're going to need some of those extra functions. The scientific calculators have many functions in addition to the basic math, adding, subtracting, multiplying, and dividing that you are used to. You would use these in science classes, but you'll also use many of these other functions to make things a lot easier. And as I mentioned, each calculator can be very, very different. You're going to have to look at the instructions and perhaps talk to your instructor to find out the exact details of how to do a specific calculation on your calculator. So that concludes our discussion on using a scientific calculator. We'll be back again next time for another topic, another math topic in science courses. So until then, have a great day, everyone, and I will see you in class.