Expert: Josh - 12/7/2010

Question
Write in scientific notation and multipy the approximate
numbers.

682,000 x 0.00024 =

I got (6.82 x 10^5) x (2.4 x 10^-4)

What do I do next and what would be final answer?

Any help in showing how to solve it with steps would go
appreciated. I've not had this type of Math in a long time.


Answer
Hi Tiffany,

You have already written the expression in scientific notations...that is good. The next step is to simplify the powers to the exponents of 10.

(6.82 x 10^5) x (2.4 x 10^-4)
= (6.82 x 2.4) x (10^5 x 10^-4) ...[1]
= (6.82 x 2.4) x 10^(5-4)
= (6.82 x 2.4) x 10^(1) ...[2]
= (13.64+2.728) x 10
= 16.368 x 10
= 163.68

[1] At this point, we apply the exponent law: x^a * x^b = x^(a+b). Here, we identify x=10, a=5 and b=-4. So, 10^5 x 10^-4 = 10^(5-4) = 10.
[2] We may proceed to calculate the product 6.82x2.4 exactly by hand, or, if we are only interested in an approximation, we can round the numbers to say 7 and 2.5 respectively. The second option will produce 6.82 x 2.4 x 10 ~= 7 x 2.5 x 10 = 17.5 x 10. The actual answer is less than 175, as we have rounded up the figures during the approximation process.

Further reading:
- A related approach is given here [http://en.wikipedia.org/wiki/Multiplication#Egyptians]