Advertisements
Advertisements
Question
The length, breadth, and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.
Solution
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 | Number | Significant Figure |
| l | 4.234 | 4 |
| b | 1.005 | 4 |
| h | 0.0201 | 3 |
Hence, area and volume both must have 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 + 0.0202005 + 0.0851034)
= 2 × 4.36
= 8.72 m2
Volume of the sheet = l × b × h
= 4.234 × 1.005 × 0.0201
= 0.085528917 m3
After rounding off = 0.0855 m3
This number has only 3 significant figures, i.e., 8, 5, and 5.
APPEARS IN
RELATED QUESTIONS
What do you mean by significant figures?
How many significant figures are present in the 0.0025?
How many significant figures are present in the 208?
How many significant figures are present in the 500.0?
How many significant figures are present in the 2.0034?
Round up the following upto three significant figures:
34.216
Round up the following upto three significant figures:
2808
How many significant figures should be present in the answer of the following calculation:-
`(0.02856 xx 298.15 xx 0.112)/0.5785`
How many significant figures should be present in the answer of the following calculation?
0.0125 + 0.7864 + 0.0215
A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?
The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?
The mass of a box measured by a grocer’s balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is
- What is the total mass of the box?
- What is the difference in the masses of the pieces to correct significant figures?
Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.
A man walking briskly in rain with speed v must slant his umbrella forward making an angle θ with the vertical. A student derives the following relation between θ and v: tan θ = v and checks that the relation has a correct limit: as v →0, θ → 0, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct? If not, guess the correct relation.
A LASER is a source of very intense, monochromatic, and unidirectional beam of light. These properties of a laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. A laser light beamed at the Moon takes 2.56 s to return after reflection at the Moon’s surface. How much is the radius of the lunar orbit around the Earth?
State the number of significant figures in the following:
0.007 m2
State the number of significant figures in the following:
2.64 × 1024 kg
State the number of significant figures in the following:
0.2370 g cm–3
Answer the following question.
Describe what is meant by significant figures.
Solve the numerical example.
A large ball 2 m in radius is made up of a rope of square cross-section with edge length 4 mm. Neglecting the air gaps in the ball, what is the total length of the rope to the nearest order of magnitude?
Solve the numerical example.
The diameter of a sphere is 2.14 cm. Calculate the volume of the sphere to the correct number of significant figures.
Write the rules for determining significant figures.
Write a short note on the following.
Rounding - off
How many significant figures should be present in the answer of the following calculations?
`(2.5 xx 1.25 xx 3.5)/2.01`
If the density of a solution is 3.12 g mL–1, the mass of 1.5 mL solution in significant figures is ______.
The number of significant figures in 0.06900 is ______.
The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give ______.
Calculate the length of the arc of a circle of radius 31.0 cm which subtends an angle of `pi/6` at the centre.
Using the rules for significant figures, the correct answer for the expression `(0.02858 xx 0.112)/(0.5702)` will be ______.
