Length of sheet, l = 4.234 m
Breadth of sheet, b = 1.005 m
Thickness of sheet, h = 2.01 cm = 0.0201 m
The given table lists the respective significant figures:
Quantity: l , Number: 4.234, Significant Figure: 4
Quantity: b , Number: 1.005, Significant Figure: 4
Quantity: h , Number: 2.01, Significant Figure : 3
Hence, area and volume both must have the least significant figures i.e., 3.
Surface area of the sheet = 2 (l × b + b × h + h × l) = 2(4.234 × 1.005 + 1.005 × 0.0201 + 0.0201 × 4.234) = 2 (4.25517 + 0.02620 + 0.08510) = 2 × 4.360 = 8.72 m2
Volume of the sheet = l × b × = 4.234 × 1.005 × 0.0201 = 0.0855 m3
This number has only 3 significant figures i.e., 8, 5, and 5.
Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = \frac{4}{3} \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \left( \frac{n_2}{2n_1} \right) \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is …….. cm.
The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy. For example, 6.658 has four significant digits. These substantial figures provide precision to the numbers. They are also termed as significant digits.