Question

The velocity of light in vacuum is $300000000 m/s$. This is expressed in standard from significant figures as
$A)\text{ }0.003\times {{10}^{11}}m/s$
$B)\text{ 300}\times {{10}^{6}}m/s$
$C)\text{ 3}.00\times {{10}^{8}}m/s$
$D)\text{ }0.03\times {{10}^{10}}m/s$

Answer 1

Hint: In the standard form of writing the value for a physical quantity, a non zero integer lying between one and ten is taken as the first significant digit and usually two digits follow the decimal places. This is then multiplied with some power of ten which gives an idea of how many trailing zeros are there in the value.

Complete answer:
The standard form of writing the value of the measurement of a physical quantity involves writing a single non zero digit between one and ten to the left of the decimal point and two digits at the right of the decimal point followed by multiplication with some power of ten which is also called as the multiplier and gives an idea about the number of trailing zeroes for the value.
This standard form notation is the most general notation and is used for all scientific purposes. The standard form is of the form
$a.bc\times {{10}^{d}}$
Where $a,b,c,d$ are integers and $a\ne 0,\left( b,c\in \left[ 0,9 \right] \right)$.
The given value of the velocity of light in vacuum is $300000000m/s$.
In the standard form, we can write this as
$3.00\times {{10}^{8}}m/s$
Hence, the standard notation of the velocity of light in vacuum is $3.00\times {{10}^{8}}m/s$.

Therefore, the correct option is $C)\text{ 3}.00\times {{10}^{8}}m/s$.

Note:
Students must remember that the first digit to the left of the decimal point in the standard notation should not be zero. If at all, they get a zero for the value of the quantity as the first digit, then they should shift the decimal place one step to the right and decrease the power of ten in the multiplier by one digit. For example, $0.30\times {{10}^{9}}m/s$ also essentially gives the same value for the velocity of light in vacuum but the standard notation should be written as $3.00\times {{10}^{8}}m/s$.