Question

How do you express $5.72\times {{10}^{4}}$ in standard form?

Answer 1

Hint: The number given in the above question, which is $5.72\times {{10}^{4}}$, consists of a number $5.72$, which lies between one and ten, multiplied by the fourth power of ten. So this means that the number is written in the scientific notation. In order to express it in the standard form, we have to multiply ${{10}^{4}}$ to the number $5.72$ and write it in the decimal form. The multiplication will be done according to sign and the value of the exponent over ten. The exponent is positive, which means that the decimal must be shifted towards the right. And the value of the exponent, equal to four, means that the decimal must be shifted four places. So overall we have to move the decimal four units towards the right.

Complete step-by-step solution:
Let us write the number given in the above question as
$\Rightarrow n=5.72\times {{10}^{4}}$
The given number is expressed as the number $5.72$ multiplied by ten raised to the power of four. So the given number is expressed in the scientific notation. For expressing it in the standard form, we have to write it in the form of decimal. For this, we have to multiply the number $5.72$ with ${{10}^{4}}$. This means that we have to shift the decimal point four units towards the right. Thus, the above number after shifting the decimal point becomes
$\Rightarrow n=57200$
Hence, the given number is expressed in the standard form as $57200$.

Note: After the decimal point, we can see only two digits to the right in the given number, and we have to shift the decimal point four units to the right. So do not be confused regarding the same as we can place as much zeroes after the rightmost digit as we want. For example, the given number can also be written as $5.7200\times {{10}^{4}}$.