Question

How do you write \[1.5 \times {10^{ - 3}}\] in standard notation?

Answer 1

Hint: The standard notation is the normal way of writing the numbers. \[1.5 \times {10^{ - 3}}\], this is the scientific way of writing the numbers. When any number has negative power then, it can be written in the denominator having numerator 1.

Complete Step by Step Solution:
We have to convert \[1.5 \times {10^{ - 3}}\] to standard notation. The number is written in scientific notation. Scientific notation can be defined as the way of expressing numbers that are too large or too small which are to be conveniently written in decimal form. In scientific notation, non – zero numbers are written in the form –
$m \times {10^n}$.
where $m$ is the non – zero real number and $n$ is an integer. The above written scientific notation can also be expressed in statements as $m$ times ten raised to the power of $n$.
To convert it in the standard notation we have to do the inverse of the above procedure.
Now, we have, \[1.5 \times {10^{ - 3}}\] there is negative power with $10$. So, when there is negative power with any number then it is put in the denominator having numerator as 1. So, ${10^{ - 3}}$ can be expressed as –
$ \Rightarrow {10^{ - 3}} = \dfrac{1}{{{{10}^3}}}$
Putting this value in the scientific notation of the number –
$
   \Rightarrow 1.5 \times {10^{ - 3}} = 1.5 \times \dfrac{1}{{{{10}^3}}} \\
   \Rightarrow 1.5 \times {10^{ - 3}} = \dfrac{{1.5}}{{1000}} \\
   \Rightarrow 1.5 \times {10^{ - 3}} = 0.0015 \\
 $

Hence, 0.0015 is the standard notation of the number \[1.5 \times {10^{ - 3}}\].

Note: While writing the number in scientific notation, we will first write the digits with decimal, then the decimal point is placed after the first digit, and then the digits after the decimal point are rounded off so that the number of digits is equal to the significant figures followed by the multiplication with 10 raised to the power number of digits that decimal places are moved.