Question

How do you express $2.74\times {{10}^{5}}$ in standard notation?

Answer 1

Hint: The notation of the number $2.74\times {{10}^{5}}$ given in the above question is the scientific notation. To express it in the standard notation, we have to write the given number in the decimal form. For this, we have to multiply \[{{10}^{5}}\] by the number $2.74$. For this, we need to consider the multiplication of a number with $10$, which shifts the decimal point one unit to the right. So the multiplication of the number $2.74$ by \[{{10}^{5}}\] means shifting the decimal point five units to the right. For this, we have to consider five digits to the right of the decimal point in the number $2.74$, which can be considered by writing $2.74$ as $2.74000$.

Complete step-by-step solution:
Let us consider the number given in the above question as
$\Rightarrow n=2.74\times {{10}^{5}}$
The above number is expressed in the form of the scientific notation, since the decimal number multiplied with \[{{10}^{5}}\] is $2.74$, which lies between one and ten. For writing the above number by \[{{10}^{5}}\], we have to multiply $2.74$ by \[{{10}^{5}}\]. We know that the multiplication of a number by ten shifts its decimal point one unit to the right. So the multiplication of the number $2.74$ by \[{{10}^{5}}\] will shift its decimal point five units to the right. So we consider five digits to the right of the decimal point by writing the above number as
$\Rightarrow n=2.74000\times {{10}^{5}}$
Now, by shifting the decimal point five units to the right, the above number will be written in the standard form as
$\Rightarrow n=274000$
Hence, the given number $2.74\times {{10}^{5}}$ is written in the standard notation as $274000$.

Note: We can consider as many zeroes as we want after the rightmost digit $4$ in the number $2.74$. We can consider this so as to make the multiplication of $2.74$ by \[{{10}^{5}}\] observable. This consideration of the decimal number also helps in preventing the calculation mistake which can be committed while multiplying $2.74$ by \[{{10}^{5}}\].