Question

How do you express $4.24\times {{10}^{2}}$ in standard form?

Answer 1

Hint: The number given in the above question is expressed in the form of the scientific notation. For expressing it in the standard form, we have to write it in the decimal form. For this, the number $4.24$ is to be multiplied by ${{10}^{2}}$, as in the given number $4.24\times {{10}^{2}}$. The multiplication with ${{10}^{2}}$ means that we have to multiply the number $4.24$ by ten, two times. The multiplication by ten means shifting of the decimal one place towards the right. So the multiplication of $4.24$ by ${{10}^{2}}$ means shifting the decimal point two places towards the right.

Complete step-by-step solution:
The number given in the above question is
$\Rightarrow n=4.24\times {{10}^{2}}$
Since the number $4.24$ is a decimal number lying between one and ten, and is multiplied by the ten squared, we can say that it is written in the scientific notation. For expressing it in the standard form, we have to write it in the decimal form. For this, we have to multiply the number $4.24$ by ${{10}^{2}}$. We know that multiplying a decimal number by ten shifts its decimal point one unit to the right, so the multiplication by ${{10}^{2}}$ will shift the decimal point of $4.24$ two units to the right. So the standard form of the above number will be
$\Rightarrow n=424$
Hence, the standard form of the given number is $424$.

Note: We must avoid the chances of calculation mistake while multiplying the number $4.24$ by ${{10}^{2}}$. We must check that the number of digits in the standard form of the number must be one greater than the exponent over ten in the scientific notation.