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Number (Intermediate) - Standard Form
 
Standard Form | Problems with Using Standard Form | Adding and Subtracting
 

Standard Form

This is a way of simplifying how very large or very small numbers are written. A number in standard form is written as:

 

A x 10n
  

Where 1 < A < 10 and n is the number of places the decimal point has moved.

Example 1: Write 253000000 in standard form.

Method:

1) Make the number between 1 and 10 by putting in a decimal point

= 2.53

2) Restore the place values by x10n n = 8
        2.53000000
           ‹———
           87654321

3) Write as 2.53 x 108

Example 2: Write 0.00000067 in standard form.

1) 6.7 (number between 1 and 10)

2) 6.7 x 10n

n = –7 ( because the point has moved the other way)
3) 6.7 x 10-7

Note - numbers less than 1 have a negative value of n.

 

Problems with Using Standard Form

Example 1: Calculate the value of (16.5 x 104) x (8 x 102) = ?

Write answers in standard form.

Using a calculator

Key sequence is as follows: 16.5 exp 7 x 8 exp 3 = 132000000

 

= 1.32 x 108

Note: the calculator sometimes writes standard form in a different way. Do not simply copy the display.


Non-calculator method

Multiply the numbers: 16.5 x 8 = 132.0

Multiply the powers 104 x 102 = 106

132 x 106 = 1.32 x 102 x 106

= 1.32 x 108


Example 2: Calculate the value of 2.4 x 1011 ÷ 1.2 x 10-4 = ?

Using a Calculator

Use the calculator in the same way but use ÷

Non-calculator method

2.4 ÷ 1.2 = 2

1011 ÷ 10-4 = 1015

2.0 x 1015
 
 
Adding and Subtracting in Standard Form

For adding and subtracting in standard form, the following methods may be applied.

Calculator: the same method but use + or –

Non-Calculator: change to ordinary numbers, do the calculations and then change the answers to standard form.