If the distance between Earth and the Moon is 384400km, write this data approximately as '2 to the power n' (find suitable n), explain with an Example, one real life application of exponents.
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Answer:
Any given real number can be written in the form m×10n in many ways: for example, 350 can be written as 3.5×102 or 35×101 or 350×100.
In normalized scientific notation (called "standard form" in the UK), the exponent n is chosen so that the absolute value of m remains at least one but less than ten (1 ≤ |m| < 10). Thus 350 is written as 3.5×102. This form allows easy comparison of numbers, as the exponent n gives the number's order of magnitude. It is the form that is required when using tables of common logarithms. In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as 5×10−1). The 10 and exponent are often omitted when the exponent is 0.
Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized form, such as engineering notation, is desired. Normalized scientific notation is often called exponential notation—although the latter term is more general and also applies when m is not restricted to the range 1 to 10 (as in engineering notation for instance) and to bases other than 10 (for example, 3.15×220).