Advertisements
Advertisements
Question
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?
Advertisements
Solution
Mass of grocer’s box = 2.300 kg
Mass of gold piece I = 20.15g = 0.02015 kg
Mass of gold piece II = 20.17 g = 0.02017 kg
(a) Total mass of the box = 2.3 + 0.02015 + 0.02017 = 2.34032 kg
In addition, the final result should retain as many decimal places as there are in the number with the least decimal places. Hence, the total mass of the box is 2.3 kg.
(b) Difference in masses = 20.17 – 20.15 = 0.02 g
In subtraction, the final result should retain as many decimal places as there are in the number with the least decimal place
APPEARS IN
RELATED QUESTIONS
How many significant figures are present in the 208?
How many significant figures are present in the 5005?
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?
5 × 5.364
A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair?
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.
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:
6.032 N m–2
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
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 a short note on the following.
Rounding - off
Which of the following measurements has 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 statements is correct about significant figures and accuracy?
A length L is measured as 125 m, which is also written as 12500 cm and 125000 mm. How many significant figures does this measurement have?
