Standard Index Form

Standard index form is also known as standard form. It is very useful when writing very big or very small numbers.

In standard form, a number is always written as:  a x 10^b

a is always between 1 and 10. b tells us how many places to move the decimal point.

For example, 81 900 000 000 000 in standard form is 8.19 x 10^13.

It's 10¹³ because the decimal point has been moved 13 places to the left to get the number to be 8.19.

0.0000012 in standard form is 0.0000012 = 1.2 x 10^-6

It’s 10^-6 because the decimal point has been moved 6 places to the right to get the number to be 1.2.

To add and subtract numbers in standard index form, convert them into ordinary numbers, do the calculation, then change them back if you want the answer in standard form.  To multiply and divide numbers in standard form, you can use the rules for multiplying and dividing powers. Remember to make sure that your answer is correctly written in standard form and adjust it if not.

Here is your homework worksheet on Standard Form.