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

- Use the standard form A × 10
^{n}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 × 10^{2 }

1000 = 1 × 10^{3}

10,000 = 1 × 10^{4}

80000 = 8 × 10^{4}

For a number to be in standard form, it must take the form A × 10^{n} 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 × 10^{4} 42 × 10^{3} 0.42 × 10^{5 } etc.

However only 4.2 × 10^{4} 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 × 10
^{4} - 46700 = 4.67 × 10
^{4} - 56 = 2.3456 × 10
^{2}

__Example 3__

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

4.2 × 10^{3} 0.35 × 10^{2} 18 × 10^{5} 6 × 10^{3} 0.01 × 10^{1}

__Solution__

__4.2 × 10 ^{3}__ 0.35 × 10

__Example 4__

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

a) 6 × 10^{7 }b) 5.67 × 10^{3}

__Solution __

a) 6 × 10^{7 }= 6 × 10 000 000 = 60 000 000

b)5.67 × 10^{3} = 5670

Lesson Content

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