Is this within a power of 10?

Question

On a lab I should have gotten 7.8 * 10^7 but I got 1.2 *10^6. Do I have to look at the number preceding the power or just see if the power that it is raised to is within 1?

EG - I know that if I would have gotten say 8.0 * 10^7 that would be within a power of 10 but is 1.2 too little? Am I over thinking this way too much?

Answer 1

7.8 * 10^7 = 78 * 10^6

you are wrong by a factor 62, bad luck!

Answer 2

It is not within a power of 10. 7.8*10^7/1.2*10^6 = 6.5*10^1

So there is over a power of 10 difference. I would suggest yu go back and check each step, and if you find nothing, go and recheck the data.

Answer 3

Well, 7.8 * 10^7/1.2 * 10^6 = 65 = 6.5 * 10. Is this within your tolerance?

Answer 4

The phrase, "within a power of 10," does not really have any mathematical meaning. So I'm guessing that what was really meant was: "within a FACTOR of 10"; or: "within an order of magnitude."

"Within a factor of 10" means that the ratio of the bigger number to the smaller number is less than or equal to 10. So you can divide the numbers to see if that condition is satisfied (as others have pointed out, the ratio is 65, so the answer is "no").

"Within an order of magnitude" is a phrase that is a little fuzzier. According to Wikipedia, two numbers differ by one order of magnitude if one is "about" 10 times the other. The best way to calculate the order of magnitude difference between two numbers is to take the base-10 log of their quotient. By that definition, your two numbers differ by 1.8 "orders of magnitude," so they are not within an order of magnitude of each other.

Answer 5

Look at the two numbers:

7.8 * 10^7 =
78,000,000

1.2 *10^6 =
1,200,000

There is a huge difference between the two number. Unfortuantely, I believe that you have calculated it wrong.