Significant Figures

 

 

 

Example

Sig. Digits

 

Sci-Notation

1

All non-zero digits are significant

 

 

 

 

 

 

 

1.589

4

 

1.589E+00

 

 

 

0.897

3

 

8.97E-01

 

 

 

36000

2

 

3.6E+04

 

 

 

 

 

 

 

2

Significant Zero's

 

 

 

 

 

a

All sandwiched zero's

13.02

4

 

1.302E+01

 

 

 

1.0002

5

 

1.0002E+00

 

 

 

10.5

3

 

1.05E+01

 

 

 

 

 

 

 

 

b

All trailing zero's preceded by a digit

5.000

4

 

5.000E+00

 

 

 

20.000

5

 

2.00000E+01

 

 

 

15.00

4

 

1.500E+01

 

 

 

 

 

 

 

3

Non significant Zero's

 

 

 

 

 

a

Leading Zeros

0.0200

3

 

2.00E-02

 

 

 

0067

2

 

6.7E+01

 

 

 

 

 

 

 

 

b

Trailing Zero's to the left of the decimal

56000

2

 

5.6E+04

 

 

point in a number without a decimal

1360

3

 

1.36E+03

 

 

point

 

 

 

 

 

 

 

 

 

 

 

 

*NOTE: Write the numbers in exponential notation if you have any doubt.  All zeros used to

 

indicate the power of 10 (order of magnitude) are not significant.

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Rounding Off

1

If the last digit to be retained in a number is followed by a number less than 5 (<5),

 

ROUND DOWN.

 

 

 

 

 

 

 

 

Round to 3 significant figures:

 

 

 

 

 

 

 

 

28.23

rounds to

28.2

 

 

 

 

 

 

578.1

rounds to

578

 

 

 

 

 

 

 

 

 

 

 

2

If the last digit to be retained in a number is followed by a number greater than 5 (>5),

 

ROUND UP.

 

 

 

 

 

 

 

 

Round to 2 significant figures:

 

 

 

 

 

 

 

 

5.998

rounds to

6.0

 

 

 

 

 

 

0.00258

rounds to

0.0026

 

 

 

 

 

 

3.6502

rounds to

3.7

 

 

 

 

 

 

 

 

 

 

 

3

If the last digit to be retained in a number is followed by 5 (0000000… implied),

 

ROUND the last digit retained to an EVEN NUMBER.

 

 

 

 

 

Round to 2 significant figures:

 

 

 

 

 

 

 

 

1.75

rounds to

1.8

 

 

 

 

 

 

1.050

rounds to

1.0

 

 

 

 

 

 

1.45

rounds to

1.4

 

 

 

 

Round to 4 significant figures:

 

 

 

 

 

 

 

 

67.835

rounds to

67.84

 

 

 

 

 

 

67.885

rounds to

67.88

 

 

 

 
 

 



Calculations

Uncertainty and Significant Figures

 

The Leaset Accurate Number (LAN) determines the number of digits to which the answer is expressed.

 

Addition and Subtraction

 

1.      The LAN is the number with the least number of digits following the decimal point.

2.      The answer (sum or difference) can have no more digits following the decimal point than the LAN.

 

         Example:

                        What is the total mass of a mixture made by mixing the following substances?

 

                                         212             g water (LAN)

                                              1.8         g salt

                                              1.88       g sugar

                                         ____________________

                                         215.98       g (incorrect)

                                         216             g (correct)

 

Multiplication and Division

 

1.         The LAN is the number with the least number of significant figures.

2.         The answer (product or quotient) can have no more significant figures than the LAN.

 

            Example:

Calculate the volume of a rectangular solid that has a length of 4.16 cm, a width of 2.2 cm, and a height of 2.00 cm.

 

            Volume = Length x Width x Height

 

            Volume = (4.16cm) (2.2cm) (2.00cm)

                                              LAN

 

            Volume = 18.304 cm3 (incorrect)

 

            Volume = 18 cm3 (correct)