WEBVTT 00:00:00.237 --> 00:00:01.166 - [Voiceover] What I want to do in this video 00:00:01.166 --> 00:00:03.441 is get a little bit of practice subtracting 00:00:03.441 --> 00:00:05.670 in scientific notation. 00:00:05.670 --> 00:00:10.670 So let's say that I have 4.1 x 10 to the -2 power. 00:00:13.077 --> 00:00:15.956 4.1 x 10 to the -2 power 00:00:15.956 --> 00:00:19.137 and from that I want to subtract, 00:00:19.137 --> 00:00:24.137 I want to subtract 2.6, 2.6 x 10 to the -3 power. 00:00:27.148 --> 00:00:29.191 Like always, I encourage you to pause this video 00:00:29.191 --> 00:00:30.700 and see if you can solve this on your own 00:00:30.700 --> 00:00:32.999 and then we could work through it together. 00:00:32.999 --> 00:00:35.344 All right, I'm assuming you've had a go it. 00:00:35.344 --> 00:00:38.130 So the easiest thing that I can think of doing 00:00:38.130 --> 00:00:40.592 is try to convert one of these numbers 00:00:40.592 --> 00:00:43.749 so that it has the same, it's being multiplied 00:00:43.749 --> 00:00:46.280 by the same power of ten as the other one. 00:00:46.280 --> 00:00:47.952 What I could think about doing, 00:00:47.952 --> 00:00:52.294 well can we express 4.1 times 10 to the -2? 00:00:52.294 --> 00:00:56.566 Can we express it as something times 10 to the -3? 00:00:56.566 --> 00:01:01.566 So we have 4.1 times 10 to the -2. 00:01:02.023 --> 00:01:06.156 Well if we want 10 to the -2 to go to 10 to the -3 00:01:06.156 --> 00:01:09.871 we would divide by 10, but we can't just divide by 10. 00:01:09.871 --> 00:01:12.146 That would literally change the value of the number. 00:01:12.146 --> 00:01:13.261 In order to not change it, we want 00:01:13.261 --> 00:01:15.351 to multiply by 10 as well. 00:01:15.351 --> 00:01:18.578 So we're multiplying by 10 and dividing by 10. 00:01:18.578 --> 00:01:21.086 I could have written it like this. 00:01:21.086 --> 00:01:24.963 I could have written 10/10 times, 00:01:24.963 --> 00:01:26.565 let me write this a little bit neater. 00:01:26.565 --> 00:01:30.536 I could have written 10/10 x this 00:01:30.536 --> 00:01:34.437 and then you take 10 x 4.1, you get 41, 00:01:34.437 --> 00:01:37.246 and then 10 to the -2 divided by 10 00:01:37.246 --> 00:01:39.095 is going to be 10 to the -3. 00:01:39.095 --> 00:01:42.554 So this right over here, this is equal to 10 x 4.1 00:01:42.554 --> 00:01:47.554 is 41 times 10 to the -3. 00:01:47.988 --> 00:01:49.218 And that makes sense. 00:01:49.218 --> 00:01:54.218 41 thousandths is the same thing as 4.1 hundredths 00:01:54.303 --> 00:01:56.672 and all we did is we multiplied this times 10 00:01:56.672 --> 00:01:58.831 and we divided this times 10. 00:01:58.831 --> 00:01:59.945 So let's rewrite this. 00:01:59.945 --> 00:02:04.945 We can rewrite it now as 41 X 10 to the -3 00:02:06.075 --> 00:02:11.075 minus 2.6, -2.6 x 10 to the -3. 00:02:15.107 --> 00:02:16.895 So now we have two things. 00:02:16.895 --> 00:02:21.702 We have 41 X 10 to the -3 - 2.6 x 10 to the -3. 00:02:21.702 --> 00:02:24.674 Well this is going to be the same thing as 00:02:24.674 --> 00:02:28.598 41 - 2.6. 00:02:28.598 --> 00:02:33.265 - 2.6, let me do it in that same color. 00:02:33.265 --> 00:02:35.331 That was purple. 00:02:35.331 --> 00:02:39.902 - 2.6, 10 to the -3. 00:02:39.902 --> 00:02:43.186 10, whoops, 10 to the -3. 00:02:43.186 --> 00:02:45.995 There's 10 to the -3 there, 10 to the -3 there. 00:02:45.995 --> 00:02:48.550 One way to think about it, I have just factored out 00:02:48.550 --> 00:02:50.895 a 10 to the -3. 00:02:50.895 --> 00:02:53.751 Now what's 41 - 2.6? 00:02:53.751 --> 00:02:58.751 Well 41 - 2 is 39, and then -.6 is going to be 38.4. 00:03:02.527 --> 00:03:05.198 38.4 and then you're going to have 00:03:05.198 --> 00:03:08.263 times 10 to the -3 power. 00:03:08.263 --> 00:03:10.979 x 10 to the -3 power. 00:03:10.979 --> 00:03:13.394 Now, this is what the product, 00:03:13.394 --> 00:03:16.041 or this is what the difference of these two numbers is 00:03:16.041 --> 00:03:18.363 but this is no longer in scientific notation. 00:03:18.363 --> 00:03:20.429 In order to be scientific notation 00:03:20.429 --> 00:03:25.429 this number right over here has to be between 1, 00:03:25.723 --> 00:03:27.859 has to be greater than or equal to 1 00:03:27.859 --> 00:03:31.876 and less than 10. 00:03:31.876 --> 00:03:34.593 So what we could do is we could divide this number 00:03:34.593 --> 00:03:36.543 right over here by 10. 00:03:36.543 --> 00:03:40.374 We can divide this by 10 and then we can multiply, 00:03:40.374 --> 00:03:42.998 then we can multi...so we could do this. 00:03:42.998 --> 00:03:46.405 We could, kind of the opposite of what we did up here. 00:03:46.405 --> 00:03:49.407 We could divide this by 10 and then multiply by 10. 00:03:49.407 --> 00:03:50.939 So if you divide by 10 and multiply by 10 00:03:50.939 --> 00:03:52.541 you're not changing the value. 00:03:52.541 --> 00:03:56.790 So 38.4 divided by 10 is 3.84 00:03:56.790 --> 00:03:58.508 and then all of this business, 00:03:58.508 --> 00:04:03.508 10 to the -3, 10 to the -3 x 10 is 10 to the -2 power. 00:04:05.103 --> 00:04:10.103 So this is going to be 3.84 x 10 to the -2 power.