How to calculate..

[taptapgrind]

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How do you estimate (without a calculator) 10^(negative #) under the square root?
For example:
The square root of:
10^(-2)
10^(-3)
10^(-4)...
10^(-9)

...or the square root of 2,5; 6.7; and so forth?

I know it has been asked before, but today the search engine has been 'temporarily disabled due to load issues'.

Thanks

 

[Mtd0588]

so, basically, you just divide what power the 10 is raised to by two.

for example, square root of 9 x 10^(-10) would be 3 x 10^(-5).

If the number is odd, then adjust the number (for lack of better words)

for example: square root of 9.0 x 10^-5.. change it to square root of 90 X 10^(-4), and solve accordingly so it equals ~9.5 X 10^(-2)

does that answer your question?

 

[taptapgrind]

Yes. Thanks Mtd0588!

I would assume that the square root of 2.7 or square root of 9.6 would work the same way?

Just basically estimate..

 

[taptapgrind]

And I came up with another question ralated to acid/base calculations..

How do you estimate if you have 10^(-2.3)? What is that equal to?
The answer is 5.0 x 10^(-3).

But how to get there?

 

[lala05]

And I came up with another question ralated to acid/base calculations..

How do you estimate if you have 10^(-2.3)? What is that equal to?
The answer is 5.0 x 10^(-3).

But how to get there?

I don't know of an easier way to solve this, so if someone has a better solution, I would love to hear it! But this is what I would do...

10^(-2.3) = 1/(10^2.3)
and 10^2.3 is the same as (10^2) x (10^0.3)
--> 1/10^2 = 1/100 (or 10^-2)
--> 10^0.3 is a little smaller than 10 ^1/3 (the third root of 10) which I would estimate to be about 2.1 (2.1 x 2.1 x 2.1 ≈ 10)
so 1/10^.3 ≈ 1/2.1, and 1/2.1 ≈ 0.48
--> Multiply: (10^-2) x (0.48) = 4.8 x 10^-3 ≈ 5.0 x 10^-3

Hope this helps!

 

[jay47]

And I came up with another question ralated to acid/base calculations..

How do you estimate if you have 10^(-2.3)? What is that equal to?
The answer is 5.0 x 10^(-3).

But how to get there?

The fastest way to do this is probably to just estimate. Estimate for 10^(-2) and realize that whatever answer you get will probably be a little larger than actual because the real number is smaller (10^-2.3 < 10^-2)

So what is root (10^-2)? That is equal to 1/ (10^2)= 1/100, root of 1/100= 1/10 or .01. You could do this in about 15 seconds in your head probably. Then look for the answer that is a smaller than .01, so .005.

Remember, 10^X, as you get closer to 3 (from 2 to 3) you get closer and closer to the actual whole number value of 10^3, but it is not a linear scale. Just graph 10^X to find out how it works.

Of course this isn't very accurate, but look at the answer choices to see how close they are. It very well could work.

If you want to get closer to the answer, then find a lower limit.