Year 10 Interactive Maths - Second Edition

Standard Form (Scientific Notation)

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).

For example, 658 = 6.58 × 10²

Note:

• We have expressed 658 as a product of 6.58 and a power of 10.  Clearly, 6.58 is between 1 and 10.  So the standard form of 658 is 6.58 × 10².
• 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.

Note:

The decimal point is shifted to the right by 2 places, and the negative of 2 appears as the index in the power of 10.

In general:

In converting a number to standard form, if the decimal point is shifted to the right p places, then the negative of p appears as a negative index in the power of 10.

Example 15

Solution:

Key Terms

standard form, scientific notation