Year 9 Interactive Maths - Second Edition

Standard Form (Scientific Notation)

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 15

Write 487 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 (or exponential 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