Lesson 7, Topic 1
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# Revision of Standard Form

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A number is said to be in standard form if the number is expressed in the form

A × 10n

Where A is a number between 1 and 10.

This is often written as 1 < A < 10 n is an integer (Positive or Negative)

In standard form, power of 10 (i.e. 10n) is often used.

Examples of positive powers of 10 are:

1 = 100

100 = 102

1000 = 103 etc

Examples of negative powers of 10

10-1 = $$\frac{1}{10} \scriptsize \: or \: 0.1$$

10-2  = $$\frac{1}{100} \scriptsize \: or \: 0.01$$

10-3  =$$\normalsize \frac{1}{1000} \scriptsize \: or \: \normalsize \frac{1}{10^3} \scriptsize = 0.001$$

Hence 3500000 can be written in standard form as 3.5 × 106

Similarly, the number 0.00000067 can be written as 6.7 × 10-7

### Example

Express the following numbers in standard form

(a) 5467
(b) 67894
(c)0.000456
(d) 0.00469

Solution

(a) $$\scriptsize 5467 \\ \scriptsize = 5.467 \: \times \: 1000\\ \scriptsize = 5.467 \: \times \: 10^3$$

(b) $$\scriptsize 67894 \\ \scriptsize = 6.7894 \: \times \: 10000\\ \scriptsize = 6.7894 \: \times \: 10^4$$

(c) $$\scriptsize 0.000456 \\ \scriptsize = 4.56 \: \times \: 0.0001 \\ \scriptsize = 4.56 \: \times \: 10^{-4}$$

(d) $$\scriptsize 0.00469 \\ \scriptsize = 4.69 \: \times \: 0.001 \\ \scriptsize = 4.69 \: \times \: 10^{-3}$$

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