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.
Advertisements
Solution
Given: 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 the least significant figures, i.e., 3.
Area of the sheet = l × b
= 4.234 × 1.005
= 4.25517 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.
RELATED QUESTIONS
How many significant figures are present in the 5005?
How many significant figures are present in the 126,000?
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:
10.4107
Round up the following upto three significant figures:
0.04597
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
You are given a thread and a metre scale. How will you estimate the diameter of the thread?
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?
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 SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine? (Speed of sound in water = 1450 m s–1).
State the number of significant figures in the following:
0.007 m2
State the number of significant figures in the following:
0.2370 g cm–3
State the number of significant figures in the following:
6.320 J
State the number of significant figures in the following:
0.0006032 m2
Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):-
the wind speed during a storm
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.
Nuclear radius R has a dependence on the mass number (A) as R =1.3 × 10-16 A1/3 m. For a nucleus of mass number A = 125, obtain the order of magnitude of R expressed in the meter.
Solve the numerical example.
Write down the number of significant figures in the following: 0.003 m2, 0.1250 gm cm-2, 6.4 x 106 m, 1.6 x 10-19 C, 9.1 x 10-31 kg.
Answer the following question.
Describe what is meant by order of magnitude.
Which of the following has the highest number of significant figures?
How many significant figures should be present in the answer of the following calculations?
`(2.5 xx 1.25 xx 3.5)/2.01`
Assertion (A): Significant figures for 0.200 is 3 where as for 200 it is 1.
Reason (R): Zero at the end or right of a number are significant provided they are not on the right side of the decimal point.
Taking into account of the significant figures, what is the value of 9.99 m – 0.0099 m?
The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is ______.
The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give ______.
Why do we have different units for the same physical quantity?
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 ______.
How many significant figures are present in the measurement 2007 grams?
Which of the following measurements has exactly two significant figures?
Which of the following measurements contains exactly two significant figures?
The radius of Earth is written as 0.64 × 10⁷ m in scientific notation. What is its order of magnitude?
Which of the following numbers has 4 significant figures?
Which of the following statements is correct about significant figures and accuracy?
