# Question #ff02f

Apr 19, 2017

A number written in scientific notation is in the form:

$a \times {10}^{b}$

Where $a$ can be any number from 1, but less than 10. It can be a single digit integer or include a decimal (such as $1.234$ or $4.321$).

b is an integer.

#### Explanation:

Where $a$ must be a single, non-zero digit before the decimal point.

$1 \le a < 10$

Any number of significant digits can be written to the right of the
decimal point.

To indicate the value of the number the single digit to the left of the decimal is multiplied by a power of ten

So scientific notation has a single digit $a$ followed by a decimal number to the right of the decimal that indicates the number of significant numbers ( those that have been actually measured) multiplied by the correct power of ten.

$a . b c d \times {10}^{e}$

For example:

$6 \textcolor{red}{3 , 400 , 000} = 6.34 \times {10}^{\textcolor{red}{7}}$

$0 \textcolor{b l u e}{.000 , 04} 89 = 4.89 \times {10}^{\textcolor{b l u e}{- 5}}$