Significant Figures and Scientific Notation


Rules for finding the significant figures in a number.

There are two methods for finding significant figures. The first uses the standard four rules; the second, just one rule.

First Method:

  1. Any non-zero number is significant. Ex. 347.68 has 5 sig figs.
  2.  
  3. A zero between two non-zero numbers is significant. Ex. 4078 has 4 sig figs.
  4.  
  5. Leading zeroes are never significant. Ex. 0.00369 has 3 sig figs.
  6.  
  7. Trailing zeroes are significant if on the right side of the decimal. Ex. 0.003470 has 4 sig figs, 370 has 2 sig figs, 370.90 has 5 sig figs (using rules 2 & 4).

Second Method:
Dot, Right; Not, Left.

If there is a Dot (decimal) in the number, then go to the far right of the number. Count every digit to the last nonzero digit. Ex. 0.0003420 Start at the far right zero, count to the 3. There are 4 sig. figs.

If there is Not a dot (decimal), then go to the far left of the number. Count every digit to the last nonzero digit. Ex. 1,003,450 Start at the far left at the 1, count to the 5. There are 6 sig. figs.

Sig. Figs in Math Operations

Addition and subtraction: When adding or subtracting numbers, round the answer to the least significant (or accurate) place.

ex. for adding w/sig figs.

Multiplication and division: After multiplying or dividing, the answer should contain the same number of sig. figs as the number with the fewest number of sig figs.


Rules for Scientific Notation:

or, Expressing Numbers with Exponents.

  1. All numbers are expressed in the form #.#### x 10#. One number is to the left of the decimal and the remainder follow the decimal. Ex. 3.45 x 105     6.984 x 10-3
  2.  
  3. With a number greater than one, count the places from the decimal to the left until only one number remains in front of the decimal. This number becomes your exponent. Don't lose any sig. figs when converting to scientific notation. The power of 10 does not count for sig. figs.
    2378 = 2.378 x 103     430.78 = 4.3078 x 102     2345.0 = 2.3450 x 103     3,100,000 = 3.1 x 106
  4.  
  5. With a number less than one, reverse the procedure. The exponent is then negative.
    0.9823 = 9.823 x 10-1     0.0000238 = 2.38 x 10-5     0.0045070 = 4.5070 x 10-3
  6.  
  7. To return to regular notation, move the decimal the number of places indicated by the exponent, to the right if the exp. is positive, to the left if the exp. is negative.
    7.345 x 102 = 734.5     2.9803 x 10-4 = 0.00029803     7.893 x 106 = 7,893,000
  8.  
  9. Proper scientific notation only has one number to the left of the decimal. If the number is not in proper form, it must be changed. The easiest way to do this is to change it into regular notation, then into proper scientific notation.
    746.987 x 103 = 746987 = 7.46987 x 105     110.98 x 10-3 = 0.11098 = 1.1098 x 10-1


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