math problem...

[mzteris]

so depending on whether I do this straight up or working with exponents I get a different answer!

And then the answer should be depicted in "scientific notation" - which I'm also struggling with. (Ok - my son is, but now he's asked mom! )


Please help!


8.86 + 1 * 10^3 / 3.610 * 10^3


if I convert the exponents to decimals I get 2454.57063711

if I work out the exponents I get 2.4542936288

which is correct (if either!) and how is that expressed in scientific notation?

Thanks much!!

[handmade34]

1. hmmm

don't the 10^3's cancel each other out??

[Richardo]

2. I get 9.137008309

If there are no parens, perform the functions in this order: Exponents, multiplication/division, addition/subtraction.

Ergo:

8.86 + 1 * 10^3 / 3.610 * 10^3 =

8.86 + ((1 * (10^3)) / (3.610 * (10^3)))
8.86 + ((1 * 1000) / (3.610 * 1000))
8.86 + (1000 / 3610)
8.86 + .277008309
9.137008309


Disclaimer: I'm a PoliSci major and generally can't math.

[handmade34]

3. I just got the same answer

9.137 (rounded)

me too... no math major here

[Mass]

5. delete

[Richardo]

6. in scientific notation: 9.137 * 10^0

...10^0 = 1, so that's 9.137*1

[Jim__]

7. delete - dupe

[mva92]

33. 0,2794626039

I think this is how it should look:
(8.86 + 1 * 10^3) / (3.610 * 10^3)
This is:
1008,86/3610
and that is...
0,2794626039
and some more numbers, but it should be written as just 0,28 unless the assignment specifically asks for something else.

[Mass]

4. Assuming there is no parenthesis and the fraction demominator is 3.610 and not 3.610 * 10 ^3

You have to use the order of operation Parenthesis Exponent Multiplication/Division Addition/substrction. Otherwise said, do first the exponent then the multiplication and division in the order they appear, and then the addition


8.86 + 1 * 10^3 / 3.610 * 10^3
8.86+1*1000/3.610*1000
8.86+1000/3.610*1000
8.86+1000000/3.61

Then do the division and then the addition.

277017.17024930747922437673130194 or 2.77 10^5

The difference with the other posters is that they assume the last 10^3 is at the denominator of the fraction, but, in the way you wrote this, it should be a multiplication.

[Richardo]

9. I see that, but ...

...if you perform multiplication before division, the 10^3 applies to the denominator (3.61), doesn't it? :shrug:

[Mass]

10. No, multiplication and division are at the same level as are addition and substraction.

Here is a similar example (it is rather fresh in my memory as my son is in HS and got in trouble on problems like that).

http://www.mathgoodies.com/lessons/vol7/order_operations.html

Example 3: Evaluate 9 - 5 ÷ (8 - 3) x 2 + 6 using the order of operations.

Solution:
Step 1: 9 - 5 ÷ (8 - 3) x 2 + 6 = 9 - 5 ÷ 5 x 2 + 6 Parentheses
Step 2: 9 - 5 ÷ 5 x 2 + 6 = 9 - 1 x 2 + 6 Division
Step 3: 9 - 1 x 2 + 6 = 9 - 2 + 6 Multiplication
Step 4: 9 - 2 + 6 = 7 + 6 Subtraction
Step 5: 7 + 6 = 13 Addition

[AKDavy]

8. Hmmmm That's not the answer I get at all

Using basic algabraic rules governing the order of operations (bracketed operations first, followed by exponents and roots, then * and /, and finally + and -), I group the operations this way:

(8.86 + ((1 * 10^3/3.610) * 10^3) = 277017.17

In scientific notation: 2.8 x 10^5 (Since the term "1" has only one significant figure (More accuracy wasn't indicated by decimal places (e.g. 1.00)), the scientific notation should technically use only one significant figure, and would be 3 x 10^5).

I'm pretty rusty, though.

[HERVEPA]

11. Richardo has it right.

It's 8.86 + (1 / 3.61) = 9.137008310249307

(Math Major 40 years ago here)

[Richardo]

12. Woo-hoo!

I am so smart! S-M-R-T!

[mzteris]

17. except I posted it "wrong"...

:cry:


It's really: (8.86 + 1.0 * 10^-3) / (3.610 * 10^-3)

[HERVEPA]

31. Just think of all the brain cells people wasted with the wrong problem.

We older folks don't have that many to spare!

[mzteris]

32. think of it as exercising

those brain cells!

:)

(methinks people who like doing math don't really care that it was the wrong problem anyways. . . )

[mzteris]

13. clarifying parenthesis:

(8.86 + 1.0 * 10^-3) / (3.610 * 10^-3)

I'm sorry - should've put those in before. :blush:

[Richardo]

14. Why I oughtta....

...I note that the sign of the exponents has changed as well. :grr:

:D

[mzteris]

16. I'm so sorry!

I didn't even realize that I'd left out the negative signs on the exponents! No wonder the answers were so different!

double :blush:

[Richardo]

18. 2454.57 or 2.45 x 10^3

[zipplewrath]

20. Confirm

2.45*10^3

One can make a case that three significant digits is all the problem deserves.

[mzteris]

22. Thank you!

Though I still don't know which way was "right" since it was the extended decimal places that was off in my answers. . .

[Henryman]

19. clarified parenthesis answer

(8.86 + 1.0x10E-3)/(3.610x10E-3) = (8.86 + 0.001)/0.00361 = 8.861/0.00361 = 2455

[OneTenthofOnePercent]

15. PEMDAS .... (order of operation execution)

In math, despite where an operation or function occurs in a statement or equation, some mathematical operation ave a higher "priority" and must be simplified or executed before the remainder of the statement or equation can be solved. The order of operations is as follows:

"PEMDAS" = Parentheses, Exponent, Multiply, Divide, Addition , & Subtraction

1) Solve all expressions within parentheses BEFORE moving on to the rest of the equation. "PEMDAS" applies within the subset of parentheses. When dealing with nested-parentheses (parentheses within parentheses) simplify or solve the innermost parentheses before solving the outermost parentheses.

2) Next, simply all exponential expressions into decimal form if possible before moving onto more basic functions. Don't be tricked by some operations like logarithms... those are merely simplified exponential expressions which also need solved before moving on.

3) Next, do all of the Multiplication & Division operations. Multiplication & division have the same priority so it doesn't matter which operations you do first.

4) Finally, you can combine the additive and subtractive quantities. Addition and subtraction have the same priority so it doesn't matter which operations you do first.

Your problem as stated: 8.86 + 1 * 10^3 / 3.610 * 10^3
No parentheses, so you'll do the exponents first: 8.86 + 1 * 1000 / 3.610 * 1000
Then do the multiply & divide: 8.86 + 0.277
Finally do the add & subtract: 9.137
Also, expressed in scientific notation: 9.137 x 10^0

Edit:

Alternate problem as stated: (8.86 + 1 * 10^-3) / (3.610 * 10^-3)
Within parentheses, you'll do the exponents first: (8.86 + 1 * .001) / (3.610 * .001)
Within parentheses, you'll do the multiply divide next: (8.86 + .001) / (.003610)
Within parentheses, you'll do the add & subtract next: 8.861 / .003610
There are no more exponents... so do the multiply divide: 2454.57
There is no addition or subtraction left.
The answer expressed in scientific notation: 2.45457 x 10^3

[shireen]

23. is there a typo?

Your problem as stated: 8.86 + 1 * 10^3 / 3.610 * 10^3
No parentheses, so you'll do the exponents first: 8.86 + 1 * 1000 / 3.610 * 1000
Then do the multiply & divide: 8.86 + 0.277
Finally do the add & subtract: 9.137
Also, expressed in scientific notation: 9.137 x 10^0

You have a typo starting on line 3 that's propagated downward. It should be 8.86 + 277008.31 = 277017.17 which can also be expressed as 2.7701717e5 :)

[OneTenthofOnePercent]

24. You are correct... I cancelled out second 1000 in the imaginary denomenator.

I suppose, as written, it would be multiplied by both 1000's.

[bananas]

26. Except they're using a variation of scientific notation

By "3.610 * 10^3" they mean "3.610e3"

[OneTenthofOnePercent]

27. Doesn't matter either way: "3.610 x 10^3" equals 3610 and "3.610e3" also equals 3610.

[bananas]

28. Except when it's in the denominator

because then you divide by 3.610 before multiplying by 10^3.

[Locrian]

21. 2454.57063712

(8.86 + 1.0 * 10^-3) / (3.610 * 10^-3) = 2454.57063712



Go here http://ttcalc.sourceforge.net/

and download TTCalc, cut and paste, it's free.

[bananas]

25. Google will do the math for you

Just paste in the formula where you would normally put the search terms.
Using the formula from post #13: (8.86 + 1.0 * 10^-3) / (3.610 * 10^-3)

http://www.google.com/search?hl=en&safe=off&q=%288.86+%2B+1.0+%2A+10%5E-3%29+%2F+%283.610+%2A+10%5E-3%29&btnG=Search

(8.86 + (1.0 * (10^(-3)))) / (3.61000 * (10^(-3))) = 2 454.57064

[mzteris]

29. ah ha!

But can it do scientific notation? !

[bananas]

30. It understands E-notation

Instead of "* 10^-3" you write "e-3"
so the formula would be (8.86 + 1.0e-3) / 3.610e-3

http://www.google.com/search?hl=en&source=hp&biw=1196&bih=739&q=%288.86+%2B+1.0e-3%29+%2F+3.610e-3&aq=f&aqi=h1&aql=&oq=

(8.86 + 1.0e-3) / 3.61000e-3 = 2 454.57064

More on E-notation in wikipedia: http://en.wikipedia.org/wiki/Scientific_notation

[chemenger]

34. Plug the equation into an EXCEL spreadsheet

If you have any doubt about the answer to this equation then plug it into a cell in an EXCEL spreadsheet exactly as you've typed it here, ie:

= 8.86 + 1 * 10^3 / 3.610 * 10^3

when you hit 'ENTER' you get the answer (which is 277017.17 rounded off to two decimal places)

The calculations are done in the following sequence:

= 8.86 + 1 * 10^3 / 3.610 * 10^3
= 8.86 + 1000/3.610 * 1000
= 8.86 + 277.008 * 1000
= 8.86 + 277008
= 277017.17