Scientists and mathematicians use standard form as a way of writing very large or very small numbers without using lots of zeros.
e.g. 148 800 000 =1.488 × 10^{8} Distance from the Earth to the Sun in km 0.000 000 001 = 1 × 10^{9} A nanogram, a billionth of a gram
Numbers written in standard form are shown in two parts, the first part as a number between 1 and 10 and the second part as a power of 10.
e.g. 327 = 3.27 × 10^{2} 0.46 = 4.6 × 10 ^{1}
Standard form and calculators
Using a typical scientific calculator, to enter a number in standard form:
Standard form  Enter 2.3 × 10^{4} into calculator  23000 
Calculations can be carried out using the button.
e.g. To calculate (3.65 × 10^{4}) × (2.67 × 10^{5}) press
^{ 9745500000 = 9.7455 × 109}
Writing ordinary numbers in standard form
Numbers between 1 and 10 do not need any movement of the decimal point and are in the form p × 10^{0}
e.g 3.6 in standard form is 3.6 × 10^{0}
For numbers less than 1 or greater than 10:
Type 
If the number is greater than 10

If the number is less than 1

Example 
45.3

0.036

Method 
Move the point one place to left to make number between 1 and 10.

Move the point two places to right to make the number between 1 and 10.

Answer 
45.3 = 4.53 × 10^{1}

0.036 = 3.6 × 10^{2}

Writing numbers in standard form as ordinary numbers
Move the decimal point by the number which is the power of 10.
For a positive power of 10 move the point to the right.
e.g. 5.34 × 10^{3} = = 5340
For a negative power of 10 move the point to the left.
e.g. 8.3 × 10^{ 2} = = 0.083