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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 comma has moved.

Example 1: Write 253000000 in standard form.

Method:

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

= 2,53

2) Restore the place values by multiplying 10ⁿ (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.

Calculator method

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.

Calculator method

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

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.