Significant Figure Rules



Significant Figure Rules

|Rule |Example |Number of Significant Figures |

|All digits other than zeros are significant |25 g |2 |

| |5.471 g |4 |

|Final zeros to the right of the decimal point are |6.10 mol |3 |

|significant |2.350 mL |4 |

|Zeros between significant digits are significant |309 mL |3 |

| |40.06 g |4 |

|In numbers smaller than 1, zeros to left or directly to |0.05 cm |1 |

|the right of the decimal point are not significant. |0.060cm |2 |

|Final zeros in a whole number may or may not be |3000 |1 |

|significant, depending on the measuring instrument. |7000 m |1 |

| | |(measurements have one estimated place and all are |

| | |significant) |

Adding or subtracting

The number of sig. figs. in the answer is dependent on the # of digits to the right of the decimal point in the numbers used in the calculation.

1.0034 + 1.002 = 1.005

The least # of digits to the right of the decimal in the starting numbers is what should appear in the answer.

2.0009375 - 1 = 1

Multiplying or dividing

The total number of significant figures in the numbers used in the calculation determines the number of sig. Figs in the answer. The number that contains the least significant figures determines how many sig. figs. should appear in the answer.

(2.3)(4.612) = 10.6-76 = 10.6

4.036 / 4.036 = 1.000

Lab Instrument Rules for Significant Figures

When using a measurement instrument, you must always estimate one place to the right from the last marking on the instrument. All figures, including the estimate are then significant.

Digital instruments require no estimates. All numbers on a digital instrument are significant, including zeroes.

Scientific Notation (Exponential notation)

Scientific notation is based on powers of the base number 10. The general format looks like:

n x 10x .

Advantages of scientific notation:

1.For very large or very small numbers they are written in a more concise manner using scientific notation.

2. Using this method makes figuring out the number of significant digits much easier.

Keep in Mind:

“n” must have one and only one digit to the left of the decimal.

“x” is the number of places that the decimal is moved to put the number into scientific notation.

If “x” is a negative number the original number was less than 1.

If “x” is a positive value the number is greater than 1.

You must have the correct number of significant figures in the number.

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