Transcript Document

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.
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.
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).
•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.
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
Example #4
Round each of the following to 3 significant digits.
a) 2.375
b) 6.7
c) 5
d) 2
e) 20
f) 200