# Lesson 1 – Positive index

### Objectives

At the end of this lesson, students should be able to:

• Use the standard form A × 10n where n is a positive or negative integer and 1 < A < 10

Change numbers into standard form and vice versa

Standard form is also known as standard index form or sometimes as scientific notation. It involves writing large numbers or very small numbers in terms of powers of 10.A

Positive Index     100 = 1 × 102

1000 = 1 × 103

10,000 = 1 × 104

80000 = 8 × 104

For a number to be in standard form, it must take the form  A × 10n where the index n is a positive or negative integer and A must lie in the range 1 < A < 10.

Example 1

42000 can be written in many different ways.

4.2 × 104       42 × 103        0.42 × 105      etc.

However only 4.2 × 104 satisfies the above conditions and therefore is the only one which is written in standard form.

Example 2

Write the following in standard form

a)6.63000                 b) 46700                   c) 234.56

Solution

1. 63000 = 6.3 × 104
2. 46700 = 4.67 × 104
3. 56 = 2.3456 × 102

Example 3

Of the numbers below, underline those which are written in standard form.

4.2 × 103       0.35 × 102    18 × 105        6 × 103           0.01 × 101

Solution

4.2 × 103       0.35 × 102    18 × 105        6 × 103           0.01 × 101

Example 4

These numbers are in standard form. Write them out in full.

a) 6 × 107   b) 5.67 × 103

Solution

a) 6 × 107 = 6 × 10 000 000 = 60 000 000

b)5.67 × 103 = 5670

Lesson Content
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