Standard Form

It would be more convenient to write

very large number such as

\(12\,390\,000\) in the form \(1.239\times {{10}^{7}}\)

and very small number such as

\(0.000\,000\,627\) in the form \(6.27\times {{10}^{-7}}\).

Such representations of numbers, \(1.239\times {{10}^{7}}\) and \(6.27\times {{10}^{-7}}\) are known as standard form.

In general, a positive number is said to be expressed in standard form when it is written as

\(A\times {{10}^{n}}\)

where \(1\le A<10\) and \(n\) is an integer.

Tip:

To write a number in standard form:

1. Move the decimal point until you get a number between 1 (inclusive) and 10 (exclusive).

2. Count the number of places you move the decimal place.

3. For very large number index, \(n>0\). (move to the left)

4. For very small number, index, \(n<0\). (move to the right)

Correction to the retained source: \(0.000000627=6.27\times10^{-7}\). For \(1\le x<10\), the standard-form exponent is 0. For a negative number, write a minus sign before the standard form of its magnitude; zero is written as 0.