### Scientific Notation

• -very large or very small numbers are difficult to work with when written in common decimal notation
• -it is possible to change the SI prefix so the number falls between 0.1 and 1000
• -for example 237 000 000 mm can be expressed as 237 km or 0.000 000 895 kg can be expressed as 0.895 mg
• -for situations where this is not possible the best method of dealing with this it the use of scientific notation
• -scientific notation expresses a number between 1 and 10 x 10 n where n represents the number of places
•  the decimal was moved from the right or left
• -for example 124 500 000 km   = 1.245 x 108 km

This value 1.245 x 108 really represents 1.245 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
1. To multiple numbers in scientific notation, multiply the coefficients and add the exponents
example  (4.73 x 105 m) (5.82 x 107) = 27.5 x 1012 m2 = 2.75 x 1013 m2  to divide two numbers in scientific notation, subtract the exponents algebraically
example   (1.842 x 106g) ÷ 1.0787 x 102g/mol) = 1.707611 x 104 mol = 1.708 x 104 mol

2.    to add or subtract numbers in scientific notation, convert the numbers so they have the same exponent as
the number with the greatest power of ten. Once this is done add or subtract the coefficients but leave the
exponent alone.

Example:
(3.42 x 106 m) + (8.53 x 103 m) = (3.42 x 106 m) + (0.00853 x 106 m) = 3.42853 x 106 m
= 3.43 x 106 m

Exercise:
1.    Convert each value into scientific notation

a)    0.000 934

b)    7 983 000 000

c)    0.000 000 000 820 57

d)    496 x 106

e)    0.000 06 x 101

f)      309 72 x 10–8

2.    Add, subtract, multiply, or divide the following problems. Express answer in scientific notation
to the correct certainty.

a)    (3.21 x 10–3 + (9.21 x 102)

b)    (8.1 x 103) + (9.21 x 102)

c)    (1.010 1 x 101) – (4.823 x 10–2)

d)    (1.209 x 106) x (8.4 x 107)

e)    (4.89 x 10–4) ÷ (3.20 x 10–2)