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Dennis Peacock
05-19-2005, 12:14 AM
The LOML and I have been working on a math problem in my oldest son's math book. I come up with one answer and the answer key provides a different answer. What do you come up with?

(3 * 10^12)(15 * 10^-2)

In otherwords:

(3 times 10 to the 12th) times (15 times 10 to the negative 2)

Please show me your work so I can see if I did this correctly. It's only been 34 years since I've done anything like this. :o

Martin Shupe
05-19-2005, 2:56 AM
I'll give it a shot...

3 x 15 is 45, but you knew that.

10 to the 12th times 10 to the -2 equals 10 to the 10th, IIRC. (you subtract --12-2=10)

So my answer is 45 followed by 10 zeros.

Here's another way to look at it...

10 to the third is 1000, 10 to the minus 2 is .01

1000 times .01 is 10, right?, so if you were to subtract (3-2), then the answer is 10 to the first, or 10.

OK, I can't wait, did I get the right answer?

(sometimes it helps to have been the last class to use a slide rule in high school)

Arnie Grammon
05-19-2005, 5:25 AM
(3 * 10^12)(15 * 10^-2) =
(3000000000000)(0.15) =
450000000000 =
4.5^11

It's been a while :rolleyes:

BTW, I did show my work.....do I get partial credit? :)

Arnie

Tony Falotico
05-19-2005, 6:38 AM
LOML just ran in here to find out what was burning. I assured her it was just dust burning off my brain! :D

I agree with both above, 4.5^11 or 45^10, same number!

John Hart
05-19-2005, 6:50 AM
I have to disagree with the above answers. It is 3 times ten to the 12th....making the first number 30 trillion (30 followed by 12 zeroes). then multiply that times .15. You get 4.5 trillion (45 followed by 11 zeroes).I think I'll need some more coffee :rolleyes:

Doug Shepard
05-19-2005, 6:51 AM
Martin, Arnie, and Tony have all got the right answers. If you're coming up with something different, then you're either fat-fingering the calculator buttons or you might be bypassing the rules regarding order of operations.
In a nutshell:
1) Things in parenthesis get calculated first. There may be other things going on inside the parenthesis that need to be addressed, but you need to treat everything in the parens as one term.
2) Exponention takes place next
3) Multiplication and division are the next priority
4) Additions and subtractions get last priority

John Hart
05-19-2005, 6:56 AM
ooops! got more coffee...now I see my error. 10 to the 12th is 1 trillion...not 10 trillion....yep...now I agree with the above answers!:o

Dennis Peacock
05-19-2005, 9:01 AM
Man....you guys are good!!!!!

The answer the book gave is 4.5 x 10^11 but I have three correct answers. :D Thanks guys.....next week we'll have another "math test" to help us all keep the "dust" out. :rolleyes: ;) :p

Doug Shepard
05-19-2005, 9:10 AM
.......next week we'll have another "math test" to help us all keep the "dust" out. :rolleyes: ;) :p

I can sure use it. My degree was in Math/Computer Science, which just means I've forgotten more math than most people ever learn.

Greg Heppeard
05-19-2005, 9:51 AM
OK Dennis, My TI-85 hasn't lied to me yet. It said 450,000,000,000

Hal Flynt
05-19-2005, 10:02 AM
HP 41c concurs with 4.5^11

Matthew Poeller
05-19-2005, 11:04 AM
The reason that you were probably getting the wrong answer is your order of operations. I got this from a Math forum that I go to when I cannot remember some of the basics:

To remember the conventional order of operations, you can think of

PEMDAS
(You might remember this as "Please excuse my dear Aunt Sally.")1

Parentheses
Exponents
Multiplication and Division

Here is the URL: http://mathforum.org/dr.math/faq/faq.order.operations.html
it is a pretty good site.

Using order of operations to solve yours you get:
(3*10^12)*(15*10^-2)
(3*1E12)*(15*.01)
(3E12)*(.15)
4.5E11

Mike Ramsey
05-19-2005, 11:05 AM
When my 10 yr old comes to me with problems like that i always refer her to my
17 yr old. :)

Randy Meijer
05-20-2005, 12:19 AM
When my 10 yr old comes to me with problems like that i always refer her to my 17 yr old. :)

There is the smartest man on this board. He knows how to delegate responsibility!!:D :D

05-20-2005, 2:35 PM
Basically, everything in that expression is mulitplied together...the order doesn't really matter.

You have a 3, a 10^12, a 15, and a 10^-2.

Don't let the fact that 3*10^12 is sort of put together as one number. It is, of course, but it can also be separated out as two distinct numbers. After all, that is what scientific notation is.

You can eyeball it from there multiplying what is easiest in your head:

3*15 is 45
10^12 * 10^-2 is 10^10 so now you have: 45*10^10.

Now you might be in a bit of a quandry as to how the exponent changes in relationship to moving the decimal! haha...that is left as an excercise for the reader! :D

Try it this way:

4.5 is 45/10 or 45*10^-1. But if I muliply by 10^-1, I need to balance that by mulitplying by 10^1. We get one from 10^-1*10^1 so we do nothing to change the equation:

45*10^-1*10^1*10^10

Now 'group' the 45*10^-1 together and you get 4.5:

4.5*10^1*10^10 = 4.5*10^11

Long-winded but you can now do it in your head very quickly.

Dennis Peacock
05-20-2005, 2:47 PM
Now that's pretty clear and a very understandable explanation. Very well done Chris.!!! ;) :D

Michael Perata
05-20-2005, 5:57 PM
Chris - Keep your day job and stay away from teaching, please. :cool: :p

Basically, everything in that expression is mulitplied together...the order doesn't really matter.

You have a 3, a 10^12, a 15, and a 10^-2.

Don't let the fact that 3*10^12 is sort of put together as one number. It is, of course, but it can also be separated out as two distinct numbers. After all, that is what scientific notation is.

You can eyeball it from there multiplying what is easiest in your head:

3*15 is 45
10^12 * 10^-2 is 10^10 so now you have: 45*10^10.

Now you might be in a bit of a quandry as to how the exponent changes in relationship to moving the decimal! haha...that is left as an excercise for the reader! :D

Try it this way:

4.5 is 45/10 or 45*10^-1. But if I muliply by 10^-1, I need to balance that by mulitplying by 10^1. We get one from 10^-1*10^1 so we do nothing to change the equation:

45*10^-1*10^1*10^10

Now 'group' the 45*10^-1 together and you get 4.5:

4.5*10^1*10^10 = 4.5*10^11

Long-winded but you can now do it in your head very quickly.

Rob Blaustein
05-21-2005, 2:48 PM
HP 41c concurs with 4.5^11

OK, I think a brief word about notation might be in order. 4.5E11 and 4.5^11 are generally not considered to be the same. Most would interpret the E11 as "scientific notation" to mean 'times 10 to the 11nth power' since calculators sometimes write it that way. But when typing an equation most math/science folks use the up arrow to mean 'to the power of' so 4.5^11 would be interpreted as '4.5 raised to the 11th power' which is very different from 4.5 x 10^11. I think the latter way of writing it (the way Dennis did when he gave the book's answer) is the better way to write it as it is less ambiguous.
-Rob

Tony Falotico
05-22-2005, 9:57 AM
OK, I think a brief word about notation might be in order. 4.5E11 and 4.5^11 are generally not considered to be the same. Most would interpret the E11 as "scientific notation" to mean 'times 10 to the 11nth power' since calculators sometimes write it that way. But when typing an equation most math/science folks use the up arrow to mean 'to the power of' so 4.5^11 would be interpreted as '4.5 raised to the 11th power' which is very different from 4.5 x 10^11. I think the latter way of writing it (the way Dennis did when he gave the book's answer) is the better way to write it as it is less ambiguous.
-Rob

Good Point Rob. :) :) You are right on.