# Scientific notation

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• Sep 5th 2010, 10:07 AM
pychon
Scientific notation
Problem is:

$(5.0028 x 10^-7) + (6.14 x 10^-10)$

If done on the calculator the result is $5.00894 x 10^-7 or 5.0090 x 10^-7$

I must be doing something incorrectly...
-Add $5.0028 + 6.14 = 11.1428$
-Add $10^-7 + 10^-10 = 10^-17$

So I get $1.1143 x 10^-16$

Anyone know what I did incorrectly?
• Sep 5th 2010, 10:24 AM
undefined
Quote:

Originally Posted by pychon
Problem is:

$(5.0028 x 10^-7) + (6.14 x 10^-10)$

If done on the calculator the result is $5.00894 x 10^-7 or 5.0090 x 10^-7$

I must be doing something incorrectly...
-Add $5.0028 + 6.14 = 11.1428$
-Add $10^-7 + 10^-10 = 10^-17$

So I get $1.1143 x 10^-16$

Anyone know what I did incorrectly?

A proper way to do it would be

$(5.0028 \cdot 10^{-7}) + (6.14 \cdot 10^{-10}) = 5002.8 \cdot 10^{-10} + 6.14 \cdot 10^{-10}$

$= 5008.94 \cdot 10^{-10} = 5.00894\cdot10^{-7}$

If working in significance arithmetic this would need to be rounded accordingly.
• Sep 5th 2010, 11:34 AM
pychon
brilliant... :)

another i'm stumbling on...

$\frac {(7.309 x 10^{-1})^2}{5.9843(2.0536 x 10^{-9})}$

doing the math:

$53.421481 x 10^{-2}$
or
$0.53421481$

$5.9843(0.0000000020536) = 1.228935848 x 10^{-8}$
or
$0.00000001228935848$

answer comes out to be $43469706.81$ , sn with my math $4.347 x 10^{7}$

calculator calculates: $4.397 x 10^{-12}$
• Sep 5th 2010, 11:44 AM
undefined
Quote:

Originally Posted by pychon
brilliant... :)

another i'm stumbling on...

$(7.309 x 10^1)^2 / 5.9843(2.0536 x 10^-9)$

doing the math:

$53.421481 x 10^-2$
or
$0.53421481$

$5.9843(0.0000000020536) = 1.228935848 x 10^-8$
or
$0.00000001228935848$

answer comes out to be $43469706.81$ , sn with my math $4.347 x 10^7$

calculator calculates: $4.397 x 10^-12$

Please clarify whether the question is to find

$\displaystyle \frac{(7.309\cdot10^1)^2}{5.9843}\cdot2.0536\cdot1 0^{-9}$

or

$\displaystyle\frac{(7.309\cdot10^1)^2}{5.9843\cdot 2.0536\cdot10^{-9}}$
• Sep 5th 2010, 11:51 AM
pychon
erm, is there a manual for properly coding the math questions? i have no clue... anyway its the second you've listed, but in parentheses

$frac{(7.309 x 10^{1})^{2} / 5.9843(2.0536 x 10^{-9})}$
• Sep 5th 2010, 12:04 PM
undefined
Quote:

Originally Posted by pychon
erm, is there a manual for properly coding the math questions? i have no clue... anyway its the second you've listed, but in parentheses

$frac{(7.309 x 10^{1})^{2} / 5.9843(2.0536 x 10^{-9})}$

What do you mean, "but in parentheses"? Adding parentheses to the expression you indicated has no effect because multiplication is associative.

For help with mathematical typesetting, see LaTeX Help Subforum.

You need to realize that $1.23 \cdot 10^{4}$ means nothing more than 1.23 multiplied by 10^4. Compute as you would any other expression involving multiplication and division. Remember rules for exponents, $x^a \cdot x^b = x^{a+b}$ and $\displaystyle\frac{x^a}{x^b}=x^{a-b}$.
• Sep 5th 2010, 12:24 PM
pychon
Yep, I located LaTex in the faq and finally now in the forum.. mods need to fix the link.

Anyway, the math is being multipled as noted... the work is all there, but suspect your suggesting not to solve the value of the power until the final result.

Also, in parentheses the denomenator is $5.9843(2.0536 x 10^{-9})$, with what you had $5.9843\cdot2.0536\cdot10^{-9}$ wouldn't that be incorrect? If there was a problem of $(10^{-5})^{3}$, wouldn't that be $10^{-15}$ not $10^{-2}$?

$\frac {(7.309 x 10^{-1})^2}{5.9843(2.0536 x 10^{-9})}$
• Sep 5th 2010, 12:43 PM
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Quote:

Originally Posted by pychon
Also, in parentheses the denomenator is $5.9843(2.0536 x 10^{-9})$, with what you had $5.9843\cdot2.0536\cdot10^{-9}$ wouldn't that be incorrect?

$5.9843\cdot2.0536\cdot10^{-9} = 5.9843(2.0536\cdot10^{-9})$

What you wrote here

Quote:

Originally Posted by pychon
If there was a problem of $(10^{-5})^{3}$, wouldn't that be $10^{-15}$ not $10^{-2}$?

does not apply since there is no power raised to another power.

Yes you should set the powers of 10 aside for efficiency purposes.

$\displaystyle\frac{(7.309\cdot10^1)^2}{5.9843\cdot 2.0536\cdot10^{-9}}= \frac{7.309^2}{5.9843\cdot2.0536}\cdot\frac{10^2}{ 10^{-9}}$

Continue from there or say if you didn't see how I did that.
• Sep 5th 2010, 01:13 PM
pychon
I see where you're going, but must be doing something wrong. If the problem is entered entirely into my calculator is comes out to $4.397\cdot10^{-12}$ and I'm not getting anything close to that.

Maybe you could check a previous problem I had, is the answer correct?
$\frac{(5.19\cdot 10^{-6})(8.3\cdot10^{5})}{2.07\cdot10^{4}}
$

$2.1\cdot10^{-4}$
• Sep 5th 2010, 01:16 PM
undefined
Quote:

Originally Posted by pychon
I see where you're going, but must be doing something wrong. If the problem is entered entirely into my calculator is comes out to $4.397\cdot10^{-12}$ and I'm not getting anything close to that.

Maybe you could check a previous problem I had, is the answer correct?
$\frac{(5.19\cdot 10^{-6})(8.3\cdot10^{5})}{2.07\cdot10^{4}}
$

$2.1\cdot10^{-4}$

You are entering it into your calculator wrong. Remember order of operations.

Yes rounded to two significant figures the last calculation is correct.
• Sep 5th 2010, 01:24 PM
pychon
I don't know how I could be entering it into the calculator incorrectly when entering the entire problem into it... as noted before the answer I received was 43469706.81 and doing my math above and following order of operations (para, powers, mult/div)
• Sep 5th 2010, 01:42 PM
undefined
Quote:

Originally Posted by pychon
I don't know how I could be entering it into the calculator incorrectly when entering the entire problem into it... as noted before the answer I received was 43469706.81 and doing my math above and following order of operations (para, powers, mult/div)

The correct answer is indeed 43469706.81 (rounded). I see you had this all along, but using the method outlined above is more efficient (at least for most of these types of problems that you would need to work out on paper). You must be typing something wrong into your calculator because $4.397\cdot10^{-12}$ is not correct.
• Sep 5th 2010, 01:53 PM
pychon
Quote:

Originally Posted by undefined
The correct answer is indeed 43469706.81 (rounded). I see you had this all along, but using the method outlined above is more efficient (at least for most of these types of problems that you would need to work out on paper). You must be typing something wrong into your calculator because $4.397\cdot10^{-12}$ is not correct.

That's what confused me... not sure how $4.397\cdot10^{-12}$ displayed, but I calculated it several times and got that and been trying to figure out how it came out to $10^{-12}$, the math I did came out to $10^{7}$... writing out the long way too... but I like your suggestion... the more efficient the better. Though $4.347\cdot10^{7}$ should be correct?
• Sep 5th 2010, 02:02 PM
undefined
Quote:

Originally Posted by pychon
That's what confused me... not sure how $4.397\cdot10^{-12}$ displayed, but I calculated it several times and got that and been trying to figure out how it came out to $10^{-12}$ over what math I did $10^{7}$... writing out the long way too... but I like your suggestion... the more efficient the better. Though $4.347\cdot10^{7}$ should be correct?

Rounded to four significant figures, yes $4.347\cdot10^{7}$ is correct.

Maybe I'm preaching to the choir but for example if you were presented with this problem

$\displaystyle \frac{6\cdot10^{-60}}{3\cdot10^{-50}}$

you would definitely not want to expand numerator and denominator separately, but rather use the method given above and immediately see that the answer is $2\cdot10^{-10}$.

As to your calculator woes, it's kind of hard to "diagnose over the phone" (meaning it would be much easier if I could see in person), but I suppose if you described what kind of calculator you have and what keystrokes you used we might get to the bottom of it.
• Sep 5th 2010, 02:02 PM
yeKciM
Quote:

Originally Posted by pychon
That's what confused me... not sure how $4.397\cdot10^{-12}$ displayed, but I calculated it several times and got that and been trying to figure out how it came out to $10^{-12}$ over what math I did $10^{7}$... writing out the long way too... but I like your suggestion... the more efficient the better. Though $4.347\cdot10^{7}$ should be correct?

correct answer is $\displaystyle \frac{(5.19\cdot 10^{-6})(8.3\cdot10^{5})}{2.07\cdot10^{4}} = 2.081 \cdot 10^{-4}$

to get it by calculator :

enter 5.16 then pres "exp" than 6 than "-" (+/- probably is written) than multiply "*" then enter 8.3 than "exp" than 5 pres "=" , than divede ( / ) than 2.07 again "exp" and 4.... press "=" again (you can do it without "=" before dividing but if you need to write down on paper .... ) than you will get 0.000208101 so now press "FIX" or something like that (depending on type of calculator , can be F -> E .... or something ) than you will get $2.081 \cdot 10^{-4}$ :D:D:D
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