Scientific notation is a quick way of writing very large or very small numbers.

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Scientific Notation Significant Digits

• Scientific notation is a quick way of writing
  very large or very small numbers.

Example 1 Write 234 000 000 m/s in scientific
notation.

• 2.34 x 108 m/s.
•  
• The decimal is moved until there is only one
  non-zero digit to the left.
• To show that the decimal has moved 8 places to
  the left, a positive exponent of 8 has been given
  to the base 10.

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Example 2 Write 0.000 000 000 478 s in
scientific notation.

• 4.78 x 10-10 s.
•  
• The decimal has been moved 10 places to the
  right. A negative exponent of 10 has been given
  to the base.

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• Significant Digits
•  In any given number, some digits are
  significant, and some are not. To decide which
  digits are which a set of rules must be followed.

• All non-zero digits are significant. (ie. 374
  has three significant digits)

• All leading zeros are not significant. (ie. 0.000
  035 has 2 significant digits).

• If there is no decimal point, all trailing zeros
  are not significant. (ie 125 000 has three
  significant digits).

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• All digits used in the coefficient of a number
  written in
• Scientific notation are significant.
• (ie. 3.500 x 103 has 4 significant digits).

The number of significant digits in the answer to
a problem should always equal the smallest number
of significant digits in the given data.
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Example 3 State the number of significant digits
in each of the following.   a) 564 b) 2500 c)
3.0     d) 1.350 e) 0.005 f) 2.00 x
102   g) 250 001 h) 0.34 i) 0.00 304 0
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• Example 4 
• Round each of the following to 3 significant
  digits.
•  
• 2.375 b) 6.7 c) 5
• d) 2 e) 20 f) 200