|
Astronomers, biologists, engineers, physicists and many others encounter
quantities whose measures involve very small or very large numbers.
For example, the distance of the earth from the sun is approximately
144,000,000,000 metres and the distance that light will travel in 1 year is
5,870,000,000,000 metres.
It is sometimes tedious to write or work with such numbers. This
difficulty is overcome by writing such numbers in standard form.
E.g. 144,000,000,000 = 1.44 × 10¹¹
5,870,000,000,000 = 5.87 × 10¹²
If a quantity is written as the product of a power of 10 and a number
that is greater than or equal to 1 and less than 10, then the quantity is
said to be expressed in standard form (or scientific notation).
It is also known as exponential form.
For example, 65 = 6.5 × 10¹
Note that we have expressed 65 as a product of 6.5 and a power of
10. Clearly, 6.5 is between 1 and 10. So the standard form of 65
is 6.5 × 10¹.
Example 24
Write 643 in standard form.
Solution:
Note:
The decimal point is shifted to the left by 2 places, and 2 appears as
the positive index in the power of 10.
In general:
In converting a number to standard form, if the decimal point is shifted
to the left p places, then p
appears as a positive index in the power of 10.
Key Terms
standard form, scientific
notation, exponential form
|
