2.1 Scientific Notation
Scientists often use numbers that are very large or very small in measurements. For
example, the Earth’s age is estimated to be about 4,500,000 (4.5 billion) years.
Numbers like these are bulky to write, so to make them more compact scientists use
powers of 10. Writing a number as the product of a number between 1 and 10 multiplied
by 10 raised to some power is called scientific notation.
To learn how to write a number in scientific notation, let’s consider the number
2468. To write this number in scientific notation:
1. Move the decimal point in the original number so that it is located after the first
nonzero digit.
2. Multiply this new number by 10 raised to the proper exponent (power). The
proper exponent is equal to the number of places that the decimal point was
moved.
3. The sign on the exponent indicates the direction the decimal was moved.
E x a m p l e 2.1
Write 5283 in scientific notation.
SOLUTION Place the decimal between the 5 and the 2. Since the decimal
was moved three places to the left, the power of 10 will be 3
and the number 5.283 is multiplied by
E x a m p l e 2.2
Write 4,500,000,000 in scientific notation (two significant figures).
SOLUTION Place the decimal between the 4 and the 5. Since the
decimal was moved nine places to the left, the power
of 10 will be 9 and the number 4.5 is multiplied by
4.5 * 109
109.
4
9
500 000 000.
5.283 * 103
103.
5283.
3
moved left : positive exponent
moved right : negative exponent
2.468 * 103
2468 : 2.468 (decimal moves three places to the left)
measurement
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