Question

How do you express $0.096$ in scientific notation?

Answer 1

Hint: As moving the decimal point by two digits to the right makes the number $9.6$ which is the valid form, it is followed by multiplication with ${{10}^{-2}}$ to make the number remain mathematically same.

Complete step-by-step solution:
The given number is $0.096$ . By scientific notation, we mean to express a given number in a decimal form such that it has a single digit to the left of the decimal sign which is a natural number and is multiplied by an integer power of $10$ . This form is developed by moving the decimal point either to the left or to the right of the number. Now, moving a decimal point is always accompanied with multiplication by an integer power of 10 so that the net product remains constant.
If we move the decimal by one digit to the right, the numbers becomes
$\Rightarrow 0.96$
The digit to the left of the decimal point is $0$ . So, we again need to move the decimal point towards the right. If we move the decimal by one digit to the right, the numbers becomes
$\Rightarrow 9.6$
The digit to the left of the decimal point is $9$ , which is non-zero. Thus, this form is valid.
Now, if we move the decimal point to the right by $n$ digits, the number is multiplied by ${{10}^{-n}}$ and if the decimal point is moved to the left by $n$ digits, the number is multiplied by ${{10}^{n}}$ . In the given problem, we have moved the decimal point by $2$ digits to the rights. Thus, we multiply the final number by ${{10}^{-2}}$ .
The number finally becomes
$\Rightarrow 9.6\times {{10}^{-2}}$
Therefore, we can conclude that $0.096$ can be expressed in the scientific notation as $9.6\times {{10}^{-2}}$.

Note: We must be very careful while moving the decimal point. Having too many zeroes in the number often creates confusion in the number of digits by which we have moved the decimal point. We must remember to multiply with the integer power of $10$ at the end.