Multiplying and dividing numbers in scientific notation

[Gringo123]

Can anybody talk me through the righ way to approach this problem? I know that the answer is 8.79 x 10 to the power of 5.

7.23 x 10 to the power of 5 x 1.09 x 10 to the power of minus 3
______________________________________________________ (divided by)

8.97 x 10 to the power of minus 4

Thanks

 

[sjb-2812]

What is 10² x 10^-3, for instance?

 

[Gringo123]

10-1 (to the power of minus 1)??

 

[sjb-2812]

Yes, that's right! So what would 10^a x 10^b be (where a and b are any number)?

 

[Gringo123]

My understanding is that you add the powers but use normal multiplication with the main numbers. So would it be: 100 a+b (a+b as powers)?

 

[sjb-2812]

Not quite, otherwise in your first example you would have written 100^-1, wouldn't you?

 

[Gringo123]

10 a+b

 

[sjb-2812]

Got it! So how about 10⁶/10² ?

 

[Gringo123]

To divde you suntract the powers so, 10 4?

 

[sjb-2812]

Going well so far, so 10^a/10^c = ?

 

[Gringo123]

10 a-c

 

[sjb-2812]

Yeap, so 10^a x 10^b / 10^c = ?

 

[Gringo123]

10 a+b-c?

 

[sjb-2812]

Indeed, so 10⁵ x 10^-3 / 10^-4 = ?

 

[Gringo123]

10 5 x 10-3 = 10 2
10 2 / 10 -4 = 10 -2

 

[sjb-2812]

No, remember for division 10^a/10^c you subtract c from a, as per posts 8 to 11, so 10²/10^-4 = ?

 

[Gringo123]

But 2 - 4 = -2 so why is it incorrect to say 10 2 / 10 -4 = 10 -2? All I have done is to subtract -4 from 2.

 

[sjb-2812]

You are not doing the sum 2 - (+)4, you are doing 2 - ^-4. Perhaps another way to look at it is how much warmer is 2°C than -4°C? Is that 2°C ?

 

[Gringo123]

No, it is 6°C. I know that 2 - (-4) = 6 so is the answer to 10 2 /10 -4 = 10 6?
Thanks for your help and patience by the way!

 

[Gringo123]

I'm starting to get it now and I can see where I went wrong the 1st time.
If you work out the decimal figures and the figures with powers separately you get;
0.879 x 10 to the power of 6.
In order to present the answer as a number larger than 1 we have remove one of the powers and used it to multiply 0.879 by 10, leaving us with 8.79 x 10 5.
Thanks again for all your help and patience.

 

[sjb-2812]

Sorted! Well done :)