Answer:
Exponential Notation
Exponential notation is an alternative method of expressing numbers.
Exponential numbers take the form an, where a is multiplied by itself n times.
A simple example is 8=23=2×2×2.
In exponential notation, a is termed the base while n is termed the power or exponent or index.
Scientific notation is a specific example of exponential numbers, 10 is almost always used as the base number.
Thus 103 means 10×10×10, while 10-3 is the notation for the reciprocal of 103 namely 1/1000.
The other name for this mathematical format is standard form ( you may have come across this in GCSE mathematics).
Expressing numbers which are not whole powers of 10 in scientific notation often requires a further multiplier, termed the coefficient (C), giving the expression in the form C ×10n.
For example, 5 ×103 is the scientific notation for the number 5000, while 3.25×102is the scientific notation for the number 325.
Similarly, 3.25×10-2 would represent
3.25 × 1
100
= 3.25
100
=0.0325.
Convention
It is scientific convention to express all such numbers as coefficients between 1 and 10 and followed by an appropriate power of 10.
Examples
35200
=
3.52 ×104 NOT 352 ×102 NOT 35.2 ×103
1750
=
1.75 ×103 NOT 175 ×10 NOT 17.5 ×102
0.0436
=
4.36 ×10-2 NOT 0.436 ×10-1 NOT 43.6 ×10-3
You should use such scientific notation whenever you express very large or very small numbers - it is a recognized form of "shorthand", and it avoids spurious accuracy e.g. writing 9 000 000 suggests that the number is exactly 9 million, in contrast to 9.0 ×106 which suggests no such accuracy beyond the first decimal place of the coefficient.
Step-by-step explanation:
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