Question

How do you divide scientific notations?

Answer 1

@mathbrz can you help me?

Answer 2

Sure.

Answer 3

Yay :)

Answer 4

Alright so I have two numbers in sci. notation:

5 x 10^5 and 2 x 10^4

Answer 5

First, let's do multiplication. What is (5x10^5 * 2x10^4)?

Let's first work it out the normal way:

500,000 * 20,000 = 10,000,000,000

(You can verify this on paper, or with a calculator.)

Answer 6

Now, let's do it the sci. notation way:

5x10^5 * 2x10^4 = (5*2)*10^(5+4) = 10x10^9 = 10,000,000,000

What did we do here? Well, when multiplying, we ADD the exponents and multiply 5 and 2.

Answer 7

so that's 10 right?

Answer 8

No, that's 10 billion. 10 x 10^9 is 10 billion.

Answer 9

10^9 is basically saying "add 9 zeros to the right of the number"

10 x 10^9 = 10,000,000,000

Answer 10

Oh, I ma in Algebra 1. Is this algebra 1?

Answer 11

*am

Answer 12

I don't remember exactly, but you should know this before Algebra 2 for sure.

Answer 13

Okay, I will know this before any kid in my class hehe. Keep going.

Answer 14

Ok. Let's start with a very small number.

Let's start with 2 x 10^1

That is

\[2\times10^1\]

.

What does that mean?

It means you are multiplying the number two by ten to the 1st power.

So what is 10 to the 1st power? \[10^1\]
?

It is just 10. So \[2 \times10^1 = 2 \times 10 = 20\]

Notice now that by looking at \[2\times10^1\], we can see that we just have to move the decimal point (which is invisible here, by the way) to the right by one ten's place, and fill that space with a zero. 2. becomes 20.

Answer 15

That is easy.

Answer 16

Good. So then, tell me, what is\[2\times10^3\]
?

Don't use a calculator. Just do what we just learned.

Answer 17

2,000

Answer 18

Great!

Answer 19

Ok. So now that you understand what basic sci. notation is, tell me, how would you solve this?

\[(2\times10^1)\times(2\times10^2) = \]

Answer 20

Before using any more complected rules, just turn each factor into normal form.

Answer 21

2*10=20 and 2*100=200 20*200=4,000^3

Answer 22

Almost! And good job, that is a great start. You made no mistakes except at the end.
20 * 200 = 4,000

That is correct.

Now you added a power of 3 to the 4,000, which means actually (4,000)*(4,000)*(4,000), and clearly 2 * 200 does not equal that large number.

Answer 23

So, 20*200 = 4,000, yes. And I think you were trying to turn that back into scientific notation, and you counted the zeros, which there are 3. But, you would have to write \[4000 = 4\times10^3\]

Answer 24

Oh, I see now.

Answer 25

But, here's a shortcut!

\[(2\times10^1)(2\times10^2) = (2\times2)\times(10^{2+1}) =(2\times2)\times(10^{3}) = (4)\times(10^{3}) = 4 \times 10^3\]

Answer 26

Follow that sequence of steps from the left to the right. I think you'll see it.

Answer 27

Sorry, it's off the page, but the final answer is:

\[4\times10^{3}\]

Answer 28

So you see what happened there? You multiplied 2 and 2 together, and then you added the powers of 10 together.

Answer 29

So is this dividing?

Answer 30

Yeah

Answer 31

That is how you perform multiplication using scientific notation. Next we will cover dividing, which is almost exactly the same.

Answer 32

:)

Answer 33

\[\frac{(2\times10^1)}{(2\times10^2)} = \frac{2}{2}\times10^{1-2} = 1 \times 10^{-1}\]

Answer 34

They made it look so hard on the worksheet :/

Answer 35

So for multiplcation, you multiplied 2 and 2 together, and added the powers. To divide, you divide the 2's and subtract the powers. You need to make sure you subtract the power in the denominator FROM the power in the numerator. Ok? There is a big difference between 1-2 and 2-1.

Answer 36

1-2 is like subtracting right?

Answer 37

Alright, so here's two problems you should work.

\[(3\times10^5)\times(4\times10^2)\]

and

\[\frac{3\times10^5}{4\times10^2}\]

Answer 38

3/4=0.75 5-2=3 so its 0.75x10^3

Answer 39

Yes, 1 minus 2 is -1.

2 minus 1 is 1.

The order matters because your answer will only be correct one way. You always put the numerator's power (the power from the top of the fraction) 1st, and subtract the power from the denominator (bottom half of fraction) from it.

Answer 40

Okay.

Answer 41

Perfect.

Answer 42

:)

Answer 43

Do you feel comfortable if you have a negative exponent? For example, \[5\times10^{-2}\]

Answer 44

You do the same thing, but you just use properties of negative numbers when using either addition or subtraction. Be careful with your signs.

Answer 45

:) Thank you. I am not the brightest at math, so I have to study a lot. I wish eyerone could explain work like you. Life would be easier.

0.05

Answer 46

*everyone

Answer 47

Great!

Answer 48

I think you're doing great and picking up concepts quickly, so I wouldn't say you're not the brightest at math. :)

Answer 49

And thank you!

Answer 50

Your welcome @mathbrz

Answer 51

I had a mathematics professor this summer who didn't speak English coherently and had very poor social skills, so I feel your pain!

Answer 52

Omg! My dream is to go to college. lol

Answer 53

You will do it. :D I believe in you.

Answer 54

Thanks :)