Question

Identify the incorrect statement among the following.

• A. A true length of $5.678\, km$ has been measured in two experiments as $5.5\, km$ and $5.51\, km$, respectively. The second measurement has more precision.
• B. Length of $1\, m$ and $0.5\, m$ have been both measured with the same absolute error of $0.01\, m$. Both the measurement are equally accurate.
• C. The numbers of significant digits in $1.6$ and $0.60$ are both two.
• D. The number $2.445$ can be rounded to two decimal place as $2.45$.

Answer 1

Answer: (B), (D)

In statement $(b)$, the percentage error in case of $1 \,m$ length is
$\frac{\Delta l_{1}}{l_{1}} \times 100=\frac{0.01}{1} \times 100=1 \%$
while in case of $0.5\, m$ length, it is
$\frac{\Delta l_{2}}{l_{2}} \times 100=\frac{0.01}{0.5} \times 100=2 \%$
As percentage error in case of $0.5\, m$ length is greater. So, the accuracy is less as compared to that of $1\, m$ length. Hence this statements is incorrect.
In statement $(d)$, according to the result of rounding off, if the number to be rounded off is $5$, then the preceding digit remains unchanged if it is even or increased by $1$ , if it is odd. So, the correct result is $2.44$. Hence, this is also an incorrect statement.
However, In statement $(a)$, as the second measured value i.e., $5.51 \,km$ is more closed to the result i.e., $5.678\, km$ so, it is more precise. Hence, this statement is correct.
Similarly, in the statement $(c)$, the significant digits in first number is $2$ and in second number is also $2$ as the trailing zero after non-zero number, having decimal point are significant. Thus, this statement is also correct.