Question

How do you write $0.00032$ in scientific notation?

Answer 1

Hint: In the problem they have asked to write the number $0.00032$ in scientific form. We know that the scientific form is the representation of a number in a product of decimal value and the exponential value of $10$ such that the decimal part contains decimal is placed after the one digit from the left side. In the given problem the given number already has the decimal point after the one digit from the left side. But the digit before the decimal is $0$ but in scientific form it should not be zero. So, we will move the decimal from left to right side by one digit and we will multiply ${{10}^{-1}}$ since it is moving from left to right, we will multiply in order to don’t change the value of the given number. We will move the digit as many times as possible until we will get the non-zero number before the decimal point by simultaneously multiplying with ${{10}^{-1}}$.

Complete step-by-step solution:
Given number, $0.00032$.
Moving the decimal point one digit by its right side and multiplying with ${{10}^{-1}}$, then we will get
$0.00032=00.0032\times {{10}^{-1}}$
Again, moving the decimal point one digit by its right side and multiplying with ${{10}^{-1}}$, then we will get
$00.0032=000.032\times {{10}^{-1}}\times {{10}^{-1}}$
Again, moving the decimal point one digit by its right side and multiplying with ${{10}^{-1}}$, then we will get
$000.032=0000.32\times {{10}^{-1}}\times {{10}^{-1}}\times {{10}^{-1}}$
Again, moving the decimal point one digit by its right side and multiplying with ${{10}^{-1}}$, then we will get
$0000.32=00003.2\times {{10}^{-1}}\times {{10}^{-1}}\times {{10}^{-1}}\times {{10}^{-1}}$
Applying the exponential rule ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$ in the above equation and neglecting the zeros before the digit which is more than zero and zeros after the decimal, then we will get
$\therefore 0.00032=3.2\times {{10}^{-4}}$

Note: We can also calculate the scientific form of the number in another method. First, we will convert the given decimal in the form of fraction. The number $0.00032$ can written as in fraction
$0.00032=\dfrac{32}{100000}$
We know that $100000={{10}^{5}}$. Substituting this value in the above equation, then we will get
$\Rightarrow 0.00032=\dfrac{32}{{{10}^{5}}}$
We know that ${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$. Applying this formula in the above equation, then we will get
$\Rightarrow 0.00032=32\times {{10}^{-5}}$
Placing a decimal point from the left side and multiplying it with $100$, then we will get
$\therefore 0.00032=3.2\times {{10}^{-4}}$
From both the methods we got the same result.