Final answer:
Abbreviations such as d, s, f, t, m, k, n, and p represent various metric prefixes in exponential notation, with each corresponding to a different power of ten used in scientific notation and exponential arithmetic. 'v' does not correspond to a standard metric prefix.
Step-by-step explanation:
The exponential notation of the various abbreviations which represent metric prefixes is used to express numbers in relation to powers of ten. Scientists and mathematicians often use these prefixes for ease when dealing with very large or small numbers. Here are the exponential notations for the given abbreviations:
- (a) d = deci, which represents 10-1
- (b) s = second, in the context of metric prefixes, this may stand for 100, as it is the base unit for time
- (c) f = femto, which represents 10-15
- (d) t = tera, which represents 1012
- (e) m = milli, which represents 10-3
- (f) k = kilo, which represents 103
- (g) n = nano, which represents 10-9
- (h) v is not a standard metric prefix; however, v often represents voltage in physics
- (i) p = pico, which represents 10-12
Understanding these prefixes and their corresponding powers of ten is essential, as they are frequently used in scientific notation and exponential arithmetic.