ORDER OF MAGNITUDE OF 2^10
Answers
Answer :An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually ten, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive. When the reference value is ten, the order of magnitude can be understood as the number of digits in the base-10 representation of the value. Similarly, if the reference value is one of certain powers of two, the magnitude can be understood as the amount of computer memory needed to store the exact integer value.
Differences in order of magnitude can be measured on a base-10 logarithmic scale in “decades” (i.e., factors of ten).[1] Examples of numbers of different magnitudes can be found at Orders of magnitude (numbers).
Explanation:Generally, the order of magnitude of a number is the smallest power of 10 used to represent that number.[2] To work out the order of magnitude of a number {\displaystyle N}N, the number is first expressed in the following form:
{\displaystyle N=a\times 10^{b}}{\displaystyle N=a\times 10^{b}}
where {\displaystyle {\frac {1}{\sqrt {10}}}\leq a<{\sqrt {10}}}{\displaystyle {\frac {1}{\sqrt {10}}}\leq a<{\sqrt {10}}}. Then, {\displaystyle b}b represents the order of magnitude of the number. The order of magnitude can be any integer. The table below enumerates the order of magnitude of some numbers in light of this definition:Number {\displaystyle N}N Expression in {\displaystyle N=a\times 10^{b}}{\displaystyle N=a\times 10^{b}} Order of magnitude {\displaystyle b}b
0.2 2 × 10−1 −1
1 1 × 100 0
5 0.5 × 101 1
6 0.6 × 101 1
31 3.1 × 101 1
32 0.32 × 102 2
999 0.999 × 103 3
1000 1 × 103 3
The geometric mean of {\displaystyle 10^{b}}10^b and {\displaystyle 10^{b+1}}{\displaystyle 10^{b+1}} .