Is this equation possible?

Apr 2018
15
0
Braintree MA
I am reading a book on Energy management and there is an equation in the book that I think is an error.

Given:
K = 42048 kWh/yr.

The equation is:
Btu = 3412 / kWh x K kW x H
= 3412 Btu /kWh x 42,048 kWh
= 143.5 x 106 Btu

That last line appears to leave out something in its left field. It does not even appear to be related to the rest of the equation.
Am I missing something, or does this look to be an error in the book?

Also, what is the general accepted method for posting the multiplication symbol when asking questions like this on this forum?

Thanks.
 

skeeter

Math Team
Jul 2011
3,360
1,850
Texas
3412 BTU's = 1 kWh

$\dfrac{3412 \text{ BTU}}{\text{kWh}} \cdot \dfrac{42048 \text{ kWh}}{\text{yr}} = 1.435 \times 10^8 \text{ BTU/yr}$

kwh_btu.jpg
 
Apr 2018
15
0
Braintree MA
Thanks Skeeter, so it 1.435 makes sense. Given the information on the first line of the formula, do you have any idea where the 106 Btu comes from? It does not appear to be part of the original equation, would you agree? I am rusty on my algebra, as it has been 30 years since I have done any formal learning in the subject. However, I do pretty well considering.

It may come from somewhere else in the lengthy word problem, but if that were the case, it should be represented by a variable on the first line of the equation.
Btu = 3412 / kWh x K kW x h

Thanks for your terrific answer and great command of the site features. I will have to learn to post better.
 

skeeter

Math Team
Jul 2011
3,360
1,850
Texas
= 143.5 x 106 Btu ...
do you have any idea where the 106 Btu comes from?
not 106, actually $10^6$

\(\displaystyle 143.5 \times 10^6 = 1.435 \times 10^8\)

the latter value is in correct scientific notation
 
Apr 2018
15
0
Braintree MA
Thank you... I completely missed it. So the book is actually correct. I really appreciate it.
 
Apr 2018
15
0
Braintree MA
Actually, the book is not correct. 106 is a typo, but technically the equation and method are correct, but poorly typed out.
1584233628774.png
Thanks.
 
Apr 2018
15
0
Braintree MA
Perhaps this is a common occurrence in typed out publications. I will be on the lookout.
I wonder if mathforums.com would be an appropriate place for an energy forum.
It's surprising how scarce any kind of energy efficiency / educational help and networking there is online.
Have a great weekend and good health to you.
 
Apr 2014
1,013
348
UK
\(\displaystyle 143.5 \times 10^6 = 1.435 \times 10^8\)

the latter value is in correct scientific notation
Agreed, however, the former is correct engineering notation :)