Question

The value of $3.00km$ in yards up to the correct significant figures and the scientific notation can be shown as,
Where$\left( 1m=1.094yards \right)$.
$\begin{aligned} & A.3.282 \\\ & B.3.28\times {{10}^{2}} \\\ & C.3.28\times {{10}^{3}} \\\ & D.\text{none of these} \\\ \end{aligned}$

Answer 1

The significant figures of a number are basically the positional notation given to the digits or numbers that is playing an important role in its measurement resolution. Compute the needed value as per the question and then as per the rules of significant figures, write the number in significant figures. This will help you in answering this question.

Complete step-by-step answer:
it has been already mentioned in the question that the relation between the metre and yards. That is we can write that,
$1m=1.0964\text{yards}$
We can convert the metre into kilometres. One metre can be converted into kilometres by dividing the kilometre by thousand. That is we can write it in an equation as,
$1km={{10}^{3}}m$
Therefore by rearranging the equation,
$1m={{10}^{-3}}km$
We can compare this with the above mentioned equation as,
$1.0964\text{yards}={{10}^{-3}}km$
Rearranging this equation will give,
$1096.4\text{yards}=1km$
Therefore we can write that,
$\begin{aligned} & 1096.4\times 3\text{yards}=3km \\\ & \Rightarrow 3km=3280.84\text{yards} \\\ & \therefore \text{3km=32}\text{.8}\times {{10}^{2}}\text{yards} \\\ \end{aligned}$
Therefore, in the scientific notation, the value of $3km$ in yards will be mentioned as,
$\text{32}\text{.8}\times {{10}^{2}}\text{=3}\text{.28}\times {{10}^{3}}$
Therefore the value of $3km$ in the scientific notation can be shown as $\text{3}\text{.28}\times {{10}^{3}}$.

So, the correct answer is “Option C”.

Note: The significant figures can be otherwise known as the significant digits. It is the accuracy of a number which is written in order as the positional notation. This will be consisting of all the digits except all the leading zeros. Trailing zeros are also not considered as they are just placed only to represent the scale of the number. Among the significant figures in a number, the one which is considered to be the most significant is the number positioned with the highest exponent value and the least significant will be the number which is positioned with the lowest exponent value.