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
- 63000 = 6.3 × 104
- 46700 = 4.67 × 104
- 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