The length and breadth of a rectangular sheet are 16.2 cm and
10.1cm, respectively. The area of the sheet in appropriate significant
figures and error is
(a) 164 ± 3 cm2
(b) 163.62 ± 2.6 cm2
(c) 163.6 ± 2.6 cm2
(d) 163.62 ± 3 cm2
please explain me what is the correct answer and how to solve it
the measurements have 3 significant digits, so the product should also have 3 significant digits. Therefore, (a).
To find the area of a rectangle, you need to multiply its length by its breadth.
Given:
Length = 16.2 cm
Breadth = 10.1 cm
Calculating the area of the sheet:
Area = Length × Breadth
Area = 16.2 cm × 10.1 cm
Area = 163.62 cm²
To determine the appropriate significant figures and error, we need to consider the least precise measurement given. In this case, the least precise measurement is the breadth, which has two decimal places.
The rule for significant figures when multiplying or dividing is to round your answer to the same number of significant figures as the least precise measurement. In this case, it means rounding the area to two decimal places.
Therefore, the area of the sheet with appropriate significant figures is 163.62 cm².
Now, let's calculate the error:
The error is equal to the uncertainty in the least precise measurement. In this case, the least precise measurement is the breadth, which is given as 10.1 cm.
The uncertainty is usually considered to be half of the smallest division on the measuring device. Since there is no information provided about the measuring device, we can assume the uncertainty to be within ±0.05 cm.
Therefore, the error is ±0.05 cm.
So, the area of the sheet in appropriate significant figures and error is:
163.62 ± 0.05 cm²
The correct answer is (b) 163.62 ± 2.6 cm².
To find the area of a rectangle, you multiply its length by its breadth. The length of the rectangular sheet is given as 16.2 cm, and the breadth is given as 10.1 cm.
Area = Length × Breadth
Area = 16.2 cm × 10.1 cm
Area = 163.62 cm2
Now, let's consider the significant figures and error. The given lengths have three significant figures: 16.2 cm and 10.1 cm. When multiplying or dividing measurements, you should round the final answer to the same number of significant figures as the measurement with the fewest significant figures. In this case, that would be three significant figures.
Rounding the area to three significant figures, we get 163.62 cm2.
Now let's look at the given answer options:
(a) 164 ± 3 cm2
(b) 163.62 ± 2.6 cm2
(c) 163.6 ± 2.6 cm2
(d) 163.62 ± 3 cm2
From our calculated area, 163.62 cm2, we can see that option (b) matches both the value and the significant figures. However, we need to also consider the error. The error is generally given as the uncertainty in the measurement.
In this case, the error is given as ± 2.6 cm2 for option (b). This means that the actual area could be 2.6 cm2 more or less than the calculated value of 163.62 cm2.
Hence, the correct answer is (b) 163.62 ± 2.6 cm2.