Order of magnitude is the magnitude of any amount, in which there is a fixed ratio in which the particular class is different to the preceding, or the succeeding class by a fixed value. This fixed value is in the form of a ratio, and the most common ratio which is used all around is the power of ten. Hence, in the most common way, we can conclude that the Order of Magnitude of a value, at a particular class, is ten times higher than its preceding class, or ten times less than its succeeding class. One most common example is the Richter scale. The Richter scale is used to measure the earthquakes, and when we commonly say that “an earthquake measuring 7 on the Richter scale has occurred”, we basically want to say that the earthquake, which has occurred is 10^7 times stronger than the earthquake on the Richter scale 1`. Like a common parameter, the Richter scale also uses a parameter of 10, for its order of magnitude.
Common Uses of Order of Magnitude: An order of magnitude is used to compare the difference on an approximate basis, but the actual difference between the magnitudes is very large. Like we just discussed in the example of earthquake, the earthquake at a scale of 3, is a hundred times more powerful than the earthquake on Richter scale one. The order of magnitude is obtained by the truncation of the value, to find the integer part of the logarithm. So, the order of magnitude becomes the power of 10 contained in the number. This value is obtained by finding the logarithm of that particular number to the base ten, and if the figure calculated is not integer, then the truncation of the total figure is done, and the integer part of the figure is the Order of Magnitude of that number. Let us consider an example. If the number 4000000 is given to us, then by finding the logarithm of the number, gives us a value of around 6.602. So, the common process as stated, the truncation of the value gives us six. Hence, the order of magnitude of the number 4,000,000 comes out to be six.
Order of Magnitude Estimate: An Order of Magnitude estimate is said to be done of those values, which are too high, to estimate their Order of Magnitude. So, an estimate of the order of magnitude is to be conducted. Let us consider an example for this as well. How, to consider an order of magnitude for human population, which lies between three and thirty billion. It is ten billion.
Extremely Large Numbers: For very large numbers, double or super logarithm, can be conducted. The first logarithm gives a very large digit, and the second logarithm gives the category of very large numbers.
Extremely Small Numbers: For very small numbers, neither of the methods cannot be suited.
However, a reciprocal method can be considered for it.