# SCIENTIFIC NOTATION RULES

RULE #1:  Standard Scientific Notation is a number from 1 to 9 followed by a decimal and the remaining significant figures and an exponent of 10 to hold place value.

Example:

5.43   x   102   =   5.43   x   100   =  543

8.65   x   10 – 3  =  8.65   x   .001   =   0.00865

****54.3   x   101  is not Standard Scientific Notation!!!

RULE #2:  When the decimal is moved to the Left the exponent gets Larger, but the value of the number stays the same.  Each place the decimal moves Changes the exponent by one (1).  If you move the decimal to the Right it makes the exponent smaller by one (1) for each place it is moved.

Example:

6000.   x   100   =   600.0   x    101   =   60.00  x  102  =  6.000  x  103  =  6000

(Note:  100  =  1)

All the previous numbers are equal, but only 6.000 x 103 is in proper Scientific Notation.

RULE #3:  To add/subtract in scientific notation, the exponents must first be the same.

Example:

(3.0            x  102) + (6.4  x  103);  since 6.4  x  103 is equal to 64.  x  102.  Now add.

(3.0  x  102)

+ (64.    x  102)

67.0  x  102    =  6.70 x  103   =   6.7  x  10 3

q       67.0  x  102 is mathematically correct, but a number in standard scientific notation can only have one number to the left of the decimal, so the decimal is moved to the left one place and one is added to the exponent.

q       Following the rules for significant figures, the answer becomes 6.7  x  103.

RULE #4:  To multiply, find the product of the numbers, then add the exponents.

Example:

(2.4 x 102) (5.5 x 10 –4)  =  ?  [2.4 x 5.5 = 13.2];  [2 + -4 = -2], so

(2.4 x 102) (5.5 x 10 –4)  =  13.2 x 10 –2  =   1.3  x  10 – 1

RULE #5:  To divide, find the quotient of the number and subtract the exponents.

Example:

(3.3  x  10 – 6) / (9.1 x 10 – 8)  =  ?  [3.3 / 9.1 = .36];  [-6 – (-8) =  2], so

(3.3  x  10 – 6) / (9.1 x 10 – 8)  =   .36  x  102  =  3.6  x  10 1