WEBVTT Kind: captions; language: en-us NOTE Treffsikkerhet: 91% (H?Y) 00:00:00.000 --> 00:00:08.100 In this video I want to explain exponential. Exponential notation is a way to write 00:00:08.100 --> 00:00:14.700 numbers, so they don't take up too much space and we see it often in statistics programs when there 00:00:14.700 --> 00:00:18.650 are very large or very small numbers involved. NOTE Treffsikkerhet: 89% (H?Y) 00:00:18.650 --> 00:00:25.500 So you may have seen numbers like these, that have the letter e in them. NOTE Treffsikkerhet: 91% (H?Y) 00:00:25.600 --> 00:00:34.800 These numbers are actually very easy to interpret if you know that e means move the decimal point. 00:00:34.800 --> 00:00:41.800 Actually, it stands for the word exponent. But for us, it means move the decimal point. You should 00:00:41.800 --> 00:00:49.300 move the decimal point as many places as the following number. So five places here or eight places 00:00:49.300 --> 00:00:50.500 here. NOTE Treffsikkerhet: 91% (H?Y) 00:00:50.500 --> 00:00:58.400 If there is a minus sign, like here, then you should move it to the left. So you end up with a very 00:00:58.400 --> 00:01:05.300 small number. If there is a plus sign or nothing like here, then you move it to the right, so you 00:01:05.300 --> 00:01:08.200 end up with a very large number. NOTE Treffsikkerhet: 91% (H?Y) 00:01:08.900 --> 00:01:18.050 So let us look at this number, which number is it? Let's follow the rules. There is no sign here, 00:01:18.050 --> 00:01:25.500 which is the same as a plus and it means we should move the decimal point to the right. NOTE Treffsikkerhet: 91% (H?Y) 00:01:25.600 --> 00:01:33.100 So the first thing we can do is to add a bunch of zeroes so that we have enough. This doesn't change 00:01:33.100 --> 00:01:37.949 our number, it's still the same number written in this way, but then we're going to start moving. 00:01:37.949 --> 00:01:43.700 So we have to move the decimal point by five places to the right. So we start with this one, which 00:01:43.700 --> 00:01:55.199 is the same and then we move 1 2 3 4 5. This is our number. We discard the NOTE Treffsikkerhet: 91% (H?Y) 00:01:55.199 --> 00:02:01.850 unneeded zeros, so any zeros after the decimal point we throw out and this is it. NOTE Treffsikkerhet: 79% (H?Y) 00:02:01.850 --> 00:02:09.600 So this number is this number. It's just a different way to write it. And in fact, if we take into 00:02:09.600 --> 00:02:16.600 account that you can have a lowercase or uppercase E. The plus sign is optional. NOTE Treffsikkerhet: 91% (H?Y) 00:02:16.600 --> 00:02:25.500 And you can also have some zeros before the exponent, in order to keep constant the amount of space 00:02:25.500 --> 00:02:33.500 taken by numbers in certain statistical programs. Then all of these numbers down here are exactly 00:02:33.500 --> 00:02:40.600 the same. They're just different ways, different variants, of writing this one. NOTE Treffsikkerhet: 91% (H?Y) 00:02:41.400 --> 00:02:49.400 What about this number? Let's follow the same steps. First of all, we see there is a minus sign this 00:02:49.400 --> 00:02:53.800 time. So we have to move the decimal point to the left. NOTE Treffsikkerhet: 82% (H?Y) 00:02:53.800 --> 00:03:00.600 So, we had a bunch of zeros to the left of our number without changing it, and then we move the 00:03:00.600 --> 00:03:13.150 decimal point. So this is our starting number and we move one, two, three, four, five, six, seven, 00:03:13.150 --> 00:03:20.200 eight. That's our number. We have an extra zero there, which we throw out and this is what were left 00:03:20.200 --> 00:03:24.149 with. So, this is just a way to write NOTE Treffsikkerhet: 85% (H?Y) 00:03:24.149 --> 00:03:30.700 this one and again, taking into account variation that we may encounter. These are all 00:03:30.700 --> 00:03:33.200 exactly the same number.