Study in science deals with both very large and very small numbers. 

DEFINE - The order of magnitude of a number is the power of 10 that is closest to the numerical value of a measurement or quantity.  

Scientific notation is how scientists write large and small numbers in an efficient manner that easily indicates the order of magnitude of the value.  A change of one order of magnitude is the same as multiplying or dividing a number by 10.  For example 3452 is one order of magnitude larger than 345.2 and two orders of magnitude larger than 34.52. 

USE - Orders of magnitude are very useful for rough estimations and they also give us a very quick indication of the difference between two quantities.  For example Einstein's mass might have been about 75 kg.   The nearest power of 10 to his mass would be 10² or 100 kg.  For comparison, the average mass of a mouse is about 0.035 kg (35 g) which is closest to 10^-2 kg and a male African elephant would be close to 10⁴ kg (here we are not saying the mass of the elephant is a whopping 10 000 kg - no elephant is that big - but rather the elephant's mass is much closer to 10 000 kg than it is to 1000 kg).

APPLY - By looking at the exponent value of the nearest power of ten, we can make simple order of magnitude comparisons.  Einstein's mass is 4 orders of magnitude (2 minus -2) or about 10⁴ times more than that of the mouse.  Compare the mass of the elephant to that of the mouse (see below for the correct response).

Order of magnitude becomes very important when we consider the range of measurements possible in our physical world.  Here are some quantities in our Universe expressed to the nearest power of 10.

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