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What number do you get if you multiply 3 by 10?

What number do you get if you multiply 3 by 10 and then multiply it by 10 again?

What number do you get if you multiply 3 by 10 three times (that is, multiply 3 by `10^3`) ?

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Ian Barbour, flikr

The order of magnitude is how many times a number must by multiplied by ten to get another number.  For example, 30000 is 4 orders of magnitude larger than 3, since 3 must be multiplied by 104 to get 30000.

Another way to look at it is that  `30000/3`  is 104.

How many orders of magnitude larger is 40000000 than 4?