Algebra

Scientific notation examples | Pre-Algebra | Khan Academy

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It always helps me see many examples of something so I thought it was harmless to see more of it Examples of scientific formula So I will write a group of numbers and then I will write them In scientific form I hope this covers most of the cases See it and at the end of this video, we’re going to do Some accounts are only there to make sure we can Calculating scientific formula. Let me write down a set of numbers Zero comma zero zero eight five two This is my first number My second number is Seven, zero, one, two Zero, zero, zero, zero, zero, zero, zero, zero, zero I just stop the zeros randomly The next number is 0.0000000 I have to draw more If you keep saying “zero,” then you may find it annoying Five, zero, zero The next issue here– there A decimal point there The next number I will write is 723 And the next one is – I have many number 7 here Let me say 0.6 Then let me write another one, to be sure We have covered all the foundations Let’s say it is 823 and let’s put a number Randomly from the zeros there So the first number, here, what do we do if we want to write a number In scientific form, that is, we will find greater An exponent of 10 that fits in If we move to the first non-zero field, i.e. This box We now count how many places are to the right of the decimal point, including this digit This will be equal That is equal to 8 – this Located here – 0.52 So everything after this phrase will be Behind the decimal point So 0.52 x 10 ^ the number of digits that we have one two Three Ten to the forces, minus three Or some other way: This is a little more .. That’s equivalent to 1/2000, right? All these are thousands We have eight and a half of them Let’s do this Let’s see how many zeros we have We have three, six, nine, twelve zeros So we want to – again, we’ll start with more Our limit The largest non-zero term In this case, you will be all this far So to the left This is 7 It will become 7.012 And equal to 7.012 x 10 raised to any power? Well, it’s going to be x ^ ^ 1 plus all of those zeros how much? We have one here Then we have 1,2,3,4,5,6,7,8,9,10,11,12 zeros To be clear We do not count only the zeros But we do after everything after the first End here So it equals 1 followed by twelve zeros So the number times 10 ^ 12 So not difficult Let’s do this We go beyond the decimal point And we find the first nonzero number It’s 5 And there is nothing on his right, so it is about 5.00, if we want to To add some precision to it But it’s 5 x, and then how many on the right, or Behind our decimal point? We have 1,2,3,4,5,6,7,8,9,10,11,12,13 and we We have to add this, fourteen 5 x 10 ^ -14 Now this number, it will probably be difficult to write In scientific form, but it is not wrong to acquire Experience What are the top 10 you can divide? Well, 100 can be divided by And you can find 100 or 10 ^ 2 by saying, well, this one It is the largest phrase, and then we have two scores behind it Because we can say 100 divided by 700 or 23 So this equals 7.23 x, we could say X 100, but we want it in scientific form, then We write it as 10 ^ 2 Now we have this number What is the first nonzero phrase? That is, so it will be 6 x Then how many phrases do we have to the right of the decimal point? We only have one So x 10 ^ -1 This makes sense for it 6 ÷ 10 is because 10 ^ -1 It is 1/10, so it equals 0.6 Another example Let me put some separators in here to make it Comfortable to look at So let’s take our biggest value here We have 8 It will be 8.23 \u200b\u200b- and we shouldn’t add The rest is because it’s just zeros– x 10 ^ – We count how many phrases are after the 8 So we have 1,2,3,4,5,6,7,8,9,10 8.23 x 10 ^ 10 I think you understand the idea now It’s straight More than just calculate this, where it is Good skill in itself, I want you to understand this case I hope that the last offer will clarify it If not, just multiply this That is, multiply by 8.23 \u200b\u200bx 10 ^ 10 and You will get the number Perhaps you will try to do it using a smaller number From 10 ^ 10 10 ^ 5 maybe And you’ll get a different number for it It will consist of 5 houses after 8 But anyway, let me solve some more examples Let’s say we have the numbers – let me put a number Too young – 0.0000064 And let me have a large number Suppose we have that number and I want to multiply it I’m going to hit it – let me suppose I have too many –32– and I’m going to put a set of zeros here I don’t know when to stop I will stop here So this, it can be hit But it’s a little difficult But let’s write it in scientific form One, I will represent these numbers in an easy way Hence, I hope you will see the multiplication process It will be simpler So this is how we can write it In scientific form? Will it be 6.4 x 10 raised to any power? one two three four five six I have to add 6 So x 10 ^ -6 How can we write this number? It will be 3.2 And then we count after the occurrence after the 3 1,2,3,4,5,6,7,8,9,10,11 So 3.2 x 10 ^ 11 If we multiply these two numbers, the result will be – Let me write it in a different color – 6.4 x 10 ^ -6 X 3.2 x 10 ^ 11 As we saw in the last show, it equals 6.4 x 3.2 I’m just changing the arrangement X 10 ^ -6 x 10 ^ 11 Now how much is the result equal to? Well, I don’t want to use a calculator until I find the result Let’s do it 6.4 x 3.2 Let’s neglect decimal point now We will add it at the end So 2 x 4 = 8, 2 x 6 = 12 We put 1 in the hand, so we get 128 We put zero here 3 x 4 = 12, put 1 in the hand 3 x 6 = 18 We get 1 here, so we have the result 192 is not it? Yeah 192 We do the addition now and we have 8, 4, 1 + 9 = 10 We put 1 in the hand So we get 2 Now, we have to calculate the numbers behind Decimal point We have a number here, and another one there So we have two numbers behind the decimal point We counted one, two So 6.4 x 3.2 = 20.48 x 10 ^ We have the same basis here, so we can combine the foundations What is -6 + 11? Equal to 10 ^ 5, right? Yeah -6 + 11 = 10 ^ 5 So the next question, you might say “we\’re done”. And indeed so This number is acceptable But the next question, is this written in scientific form? And if you want to be very precise about this, it is not In scientific form, because we have a number Perhaps it can be simplified for more We could write this – let me use this method Let me divide this by 10 Any number we can multiply and divide by 10 So we can rewrite this way We can write 1/10 to this side and then multiply 10 on that side, right? This does not change the value of the number We divide by 10 and multiply by 10 This is like multiplying by 1 or dividing by 1 If you divide this side by 10, you get 2.048 We multiply this side by 10 and get x 10 ^ – x 10 means x 10 ^ 1 We can add the foundations X 10 ^ 6 And now, if we are subtle about this, we’ve got Good scientific formula here Now, we have finished several strikes Let’s divide Let me divide this number by that If we have 3.2 x 10 ^ 11 / 6.4 x 10 ^ -6, how much is it equal to? Well, this is equal to 3.2 / 6.4 We can separate them because this is a bonding property So, this is x 10 ^ 11 / 10 ^ -6, right? If we multiply these two numbers We will get this output 3.2 / 6.4 Equal to 0.5, right? 32 is equal to half of 64, or 3.2 is half of 6.4 so this Equals 0.5 and what is that? This is 10 ^ 11/10 ^ -6 So when we have a number in the denominator It can be written like this This equals 10 ^ 11/10 ^ -6 It equals 10 ^ 11 x (10 ^ -6) ^ – 1 Or, this is equal to 10 ^ 11 x 10 ^ 6 What have you done here? This is 1/10 ^ -6 So 1 / number = this number Up to Force -1 Then we hit the foundations Think like this, and it will equal 10 to the power of 17 Another way of thinking. If you have the same basis, which is 10, we divide them We take the 1 in the numerator and subtract Exponent in the place So it equals 11 – 6, so it becomes 11 + 6 = 17 So the division process ends with the result 0.5 x 10 ^ 17 It is the correct result, but if you want to be More accurate and write it in scientific form, so we want A number may be greater than this And the way we’re going to do that, let’s hit it With 10 on this side We divide by 10 on this side, or multiply by 1/10 And remember, we don’t change the value of the number if we multiply By 10 and divide by 10 We write the result using different parts So this side becomes 10 I’ll write in pink 10 X 0.5 = 5, x 10 ^ 17 ÷ 10 This equals 10 ^ 17 x 10 ^ 1, right? This is 10 ^ -1 So it equals 10 ^ 16 This is the output when we divide These two numbers are here I hope that these examples have worked on filling up Gaps involved In scientific form If I do not explain something, do not hesitate to write it in a comment on This offer or sent it to me via e-mail

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