Question

Two statements are:
$\left(1\right)$ Out of the two measurements, $50.14\text{cm}$ and $50.1\text{cm}$, the first one has greater accuracy.
$\left(2\right)$ If one travels $478\text{km}$ by rail and $850\text{m}$ by road then the total distance travelled is $479\text{km}$ in appropriate significant figures.

• A. Both the statements are correct
• B. Only statement $\left(1\right)$ is correct
• C. Only statement $\left(2\right)$ is correct
• D. Both the statements are wrong

Answer 1

The correct option is A Both the statements are correct

We know that accuracy depends on the number of significant figures. More the number of significant figures more is the accuracy of the measurement.
In case, the number of significant figures are equal then more the closeness of measurement to the true value more is the accuracy and vice-versa.
Here, $50.14\text{cm}$ have four significant figures and $50.1\text{cm}$ have three significant figures. Thus, $50.14\text{cm}$ is more accurate.

Total distance travelled $=478\text{km}+850\text{m}$
$=478\text{km}+0.850\text{km}=478.850\text{km}$
We know that in addition or subtraction, the final answer should have as many decimal places as in given data with minimum decimal places.
Here, $478\text{km}$ have no decimal point. Therefore, the final answer should have no decimal point.
On rounding off $478.850\text{km}$ to no decimal point, we get, $479\text{km}$.