# Math Help - Need help understanding this figure

1. ## Need help understanding this figure

Hello,
I am doing some reading on Radon and am having trouble understanding some of the math. Never was good at it, and it is becoming a major handicap with this project.

13.1 Bq m[-2] h[-1]
Does the above info read square meters or does it read 100ths of a meter? M 2 I can understand, I think, as meaning squared meters, but the use of a negative number is what throws me.

Am I wrong in thinking this value stands or 13.1 Bq per 100th of a meter per hour, or is it a tenth of an hour?

Thanks for any who take the time,
Al

2. Do you mean $m^{-2}$?

Remember with negative exponents
$m^{-2} = \frac{1}{m^{2}}$

3. Boy, I must have sounded too smart when asking that question..... Can you tell me that again, this time assuming I am completely ignorant?

I copied and pasted the value out of the study, so assume the value was written properly.

Thanks,
Al

4. That is the property of negative exponents

$10^{-2} = \frac{1}{100}$

So to simplify what your equation is (if I understand it correctly) would be:

$\frac{bq}{hm^{2}}$

because it would be

$bqh^{-1}m^{-2}$

and we'll just send h and m to the bottom because of that property.

5. Originally Posted by carpentershop
Hello,
I am doing some reading on Radon and am having trouble understanding some of the math. Never was good at it, and it is becoming a major handicap with this project.

13.1 Bq m[-2] h[-1]
...
Hi,

this information means: 13.1 Becquerel per square-meter per hour.

A negative exponent can be transformed into a fraction with the numerator 1:

$a^{-k}=\frac{1}{a^k}$

Therefore you can transribe your information:

$13.1\ Bq\ m[-2]\ h[-1] = 13.1\ \frac{Bq}{m^2 \cdot h}$

6. Is there a reason they don't reduce it in the first place?

So 13.1 per hour per square meter.. two square meters and 24 hours gives you 6288 Bq emitted radon.

Is there a reason to express it as you did, with the Bq over the m 2 . h ? To a math challenge guy, that looks like square meters times hours divided by Bq....

Thanks for the patience and the help.

I think I got it, Bq per square meter per hour....

7. Originally Posted by carpentershop
Is there a reason they don't reduce it in the first place?...
Hello,

of course: To print fractions is quite difficult (and a fraction wastes a lot of precious paper )

Originally Posted by carpentershop
...

So 13.1 per hour per square meter.. two square meters and 24 hours gives you 6288 Bq emitted radon....
You got it!

Originally Posted by carpentershop
...

Is there a reason to express it as you did, with the Bq over the m 2 . h ? ...
Normally a (technical) value consists of a measuring number and the name of the units. The name of the unit in your case is Becquerel per square-meter per hour. so I put all parts together and separated it from the measured value.
I'll give you (mathematically) equal expressions:

$13.1\ Bc \cdot m^{-2} \cdot h^{-1} = 13.1\ Bc \cdot \frac1m^2 \cdot \frac1h = 13.1\ Bc \cdot \frac{1}{m^2 \cdot h} = 13.1\ \frac{Bc}{m^2 \cdot h}$