SIGNIFICANT DIGITS AND SCIENTIFIC NOTATION

SIGNIFICANT DIGITS (also known as scientific figures)

Significant digits are connected to rounding. We use this so that we know what the significant digits are. What really are the important digits in a group of numbers. Here you will also findout when the zeros will be considered significant and not how it will happen. 

   

RULES FOR SIGNIFICANT DIGITS:

1. ALL none zero numbers are ALWAYS significant.

ex. 1,2,3,4,5,6,7,8,9

2. ALL zeros between non-zero numbers are ALWAYS significant.

ex. 5160003487347000006

3. ALL zeros before the 1st non-zero digit are non significant.

ex. 0.00463

4. ALL zeros after the last non-zero digit MAY OR MAY NOT BE significant.

ex. 341.20 and 100

5. ALL zeros at the right of the decimal point and at the end of the number are always significant

ex. 0000000000000000000.98045 and 0.00000000000000000000

6. ALL zeros which are to the left of a written decimal point and are in number greater than or equal to 10 are ALWAYS significant.

ex. 10.0

EXERCISES!!!: (on a 1/8 sheet of paper, state on every blank how many significant digits there are in each number) 

__________ 1) 45,000,000,000,000

__________ 2)100,708,300.000 

__________ 3)000002.048000000000

__________ 4)9.00

__________ 5)23,000,000,000.000000

So now we will move on and we will tell you about

SCIENTIFIC NOTATION

Scientific Notation simply makes answers shorter and faster to write. There will be less numbers.  

A number is in Scientific Notation if it has been expressed in the form: a x 10 raised to the power b where 1 < = a > 10 and b is an integer. The following table presents examples and how they may be expressed in scientific notation. 

     Numbers                                           Scientific Notation     

                   123                                          1.23 x 10 raised to the power of 2

                         0.0234                                     2.34 x 10 raised to the power of -2    

                       1230000                                  1.23 x 10 raised to the power of 6     

                   0.000321                                  3.21 x 10 raised to the power of -4

Here for example you have 123 and you have to transform it into scientific notation. You have to get the first significant digit which is 1 and move the decimal 2 places to the left so you can come up with the answer that you can see in the table above. 10 is always the base. The sign of the exponent depends on where you are moving the decimal point. If you are moving the decimal to the right then it becomes negative. To the left it becomes positive.

EXERCISES!!!! ( Try solving these on a 1/4 sheet of paper)

_______________ 1) 300

_______________ 2) 4,000

_______________ 3) 5,720,000,000

_______________ 4) 0.0000000006

_______________ 5) 703,421,000,000,000.000

_______________ 6) 000.000000000000858

_______________ 7) 000.000708

_______________ 8) 143,000,000.000

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