Significant Figures : Addition, Substraction, Multiplication and Division of Significant Figures

Significant Figures

 

1. Addition and Substraction of Significant Figures

 

The result  of addition and substraction has only in questionable (quesstimate). If the entire numbers are not underlined, the last is the number in questionable.

For example :

• Sampel 1

25300 g  (the 3 is in questionable)
  4140 g  (the 0 is in questionable)
______₊
29440     ( it has two numbers in questionable)
Since the final result has to have one number questionable, that number is rounded into 29,400.

• Sampel 2

152.227 cm  (the 7 is in questionable)
  22.5     cm   (the 5 is in questionable)
______₊
174.727 cm  (the final result is rounded into 174,7 cm)

• Sampel 3

523.467 cm 
  15.300 cm
______ _-
508.167 cm  (is rounded into 508.2)

• Sampel 3

430 g
255 g
______ _-
175 g  (the final result is rounded into 180 g ; a number is questionable)

2. The Multiplication and Division of Significant Figures

 

Total significant figures resulting from the addition, subcraction, multplication, division or combination is as many as one of the significant figures that has the least significant figure. Else, the counting result can only have once number in questionable.

 

1) Multiplication

a) 2.35 cm x 2.4 cm  = 5.64 cm²

                                         = 5.6 cm2 (two significant figures)

b) 0.534 cm x 5.2 cm  = 2.7768 cm²

                                            = 2.8 cm² (two significant figures)

c) 0.323 cm x 2.5 cm  = 0.8075 cm²

                                            = 0.81 cm² (two significant figures)

d) 12.5 cm x 4.5 cm x 1.23 cm  = 69.1875 cm³

                                                             = 69 cm³ (two significant figures)

e) 16.40 cm x  4.5 cm x 3.26 cm  = 240.588 cm³

                                                                  = 240 cm² (two significant figures)

F) Multiplication of significant figures with the definite numbers is describe as the following

      The thickness of a stone is 10.33 cm. If there are 17 stones arrange upright, the height of the arrangement is 10.33 cm x 17 = 175.65 becomes 175.6 cm (four significant figures)

 

2) Division

a) 52,500 g : 2.4 cm³  = 21,875g/cm³

                                            = 22,000

                                            = 2.2 x 10³ g/cm³ (two significant figures)

b) 13,550 dyne : 234 cm²  = 57.905983 dyne/cm³

                                                    = 58 dyne/cm³ (two significant figures)

 

3) Draw  the root of significant figures is as the following example

a) √625 cm  = 25.0 cm (three significant figures)

b) ³√78 cm  = 4.2726 cm
                         = 4.3 cm (two significant figures)

4) π (phi) number has value of 3.14159265

For physics counting, the total numbers behind the point from π number depends on the precision of the measuring tool.

a) Circumference of a circle the radius of  r = 12.35 is
 S = 2πr
    = 2 x (3.141) x (12.35)
 S = 77.58 cm (four significant figures)

b) Area of circle with the radius of 12.35 is
A = πr2
    = (3.141) x (12.35)2 = 479.07317 cm²
A = 479.1 cm² (four significant figures)