Identify the incorrect statement among the following.

Options

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 meausred 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

B, D

Explanation

In statement (b), the percentage error in case of 1 m length is
`(Delta l_(1))/l_(1)xx100=0.01/1xx100=1%`
while in case of 0.5 m length, it is
`(Delta l_(2))/l_(2)xx100=0.01/0.5xx100=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 preseding 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., 5.5 1 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 digit in first number is 2 and in second number is also 2 as the tralling zero after non-zero number, having decimal point are significant. thus, this statement is also correct.