6. Scientific Notation
Scientific notation (also known as standard form) is used for numbers that are either very large or very small, like:
The mass of the earth is about
6 000 000 000 000 000 000 000 000 kg
X-rays have a wavelength of about
0.000 000 095 cm
Scientific notation is a more convenient way of expressing such numbers for working with calculators and computers.
Scientific Notation - Definition
A number in scientific notation is expressed as
P × 10k where: 1 ≤ P < 10 and k is an integer
Example 1
(a) 340 000 (ordinary notation)
= 3.4 × 100 000
= 3.4 × 105 (scientific notation)
(b) 0.017 (ordinary notation)
= 1.7 ÷ 100
= 1.7 × 10-2 (scientific notation)
(c) 6.82 (ordinary notation)
= 6.82 × 1
= 6.82 × 100 (scientific notation)
To change a number from scientific notation to ordinary
notation, we simply reverse the procedure shown in Example
1.
Example 2
A computer is able to process 803 000 bits of data in
0.000 005 25 s. The rate of processing the data in is:
Our final answer is in scientific notation.
Example 3
(7 × 1011) × (6 × 10-3)
= 42 × 108 (not scientific notation!)
= 4.2 × 109
Exercises
Perform the following calculations using a calculator, by first expressing all numbers in scientific notation:
(1) 28 000 × 2 000 000 000
(2) 
Perform the following calculations using a calculator:
(3) 
(4) 
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