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Scientific Notation
A real number X expressed in scientific notation has the
format
X = a × 10k, where 1 £ |a| < 10 and k is an integer
Example:
1,201,000,000,000 = 1.201 × 1012
0.00000000000035 = 3.5 × 10-13
-1345.89 = -1.34589 × 10-3
To convert a real number from standard notation to scientific
notation
(a × 10k), the
following procedure is useful:
(1) If the real number is not already in decimal form, convert
it to a decimal number, terminating, repeating or otherwise. Note
the location of the decimal point.
(2) Determine the first nonzero digit in the number. Place a
marker immediately after this digit.
(3) Starting at the marker, count the number of places to the
decimal point. If the movement is to the right, the count is
considered to be positive; if the movement is to the left, the
count is considered negative. If no movement is need, the count
is zero.
(4) The marker indicates the location of the decimal point in the
factor a. The count represents the exponent k to be used as the
power of 10.
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