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:

math formula

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) math formula


Perform the following calculations using a calculator:

(3) math formula

(4) math formula


Answer




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