Question

How do you write the numerical value of $1.75\times {{10}^{-3}}$

Answer 1

Hint: We will first understand the concept of the scientific notation then we will use methods to convert a given scientific notation into numerical value. Since, scientific notation consists of mantissa and exponents part so we will first convert exponential form into decimal form and then we will multiply it with mantissa.

Complete step-by-step solution:
We will first understand the concept of scientific notation. Scientific notation is the way of writing the given a very large or small number. A number can be written in scientific notation when a number between 1 to 10 (also known as mantissa of the number given) is multiplied by the power of 10. The general form of scientific notation is $a\times {{10}^{b}}$, where ‘a’ is a number between 1 to 10, also known as the mantissa of a number and ‘b’ is an integral number.
Now, we have to convert the scientific notation $1.75\times {{10}^{-3}}$ into numerical form.
At first, we will find the mantissa of the given number by comparing it with the general form $a\times {{10}^{b}}$.
In $1.75\times {{10}^{-3}}$ we can say that mantissa is 1.75 and the exponential part is ${{10}^{-3}}$.
Now, we know that when we have negative power then it fraction and so we can write ${{10}^{-3}}$ as $\dfrac{1}{1000}$.
$\Rightarrow 1.75\times {{10}^{-3}}=1.75\times \dfrac{1}{1000}$
$\Rightarrow 1.75\times {{10}^{-3}}=1.75\times 0.001$
$\Rightarrow 1.75\times {{10}^{-3}}=0.00175$
Hence, the numerical value of $1.75\times {{10}^{-3}}$ is 0.00175.
This is our required solution.

Note: Students are required to note that in scientific notation mantissa always lies between 1 to 10 and its value cannot exceed 10. Also, note that we usually write scientific notation so that we can compare the number easily by just seeing the power of 10. When we have negative power of 10 then the smaller the power bigger is the number. For example: We have two number $3\times {{10}^{-3}}$ and $4\times {{10}^{-5}}$, then we will have that $3\times {{10}^{-3}}$ is greater than $4\times {{10}^{-5}}$ because -3 is greater than -5.