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प्रश्न
Describe what is meant by significant figures.
What do you mean by significant figures?
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उत्तर १
Significant figures:
- Significant figures in the measured value of a physical quantity are the sum of reliable digits and the first uncertain digit.
OR
The number of digits in a measurement about which we are certain, plus one additional digit, the first one about which we are not certain, is known as significant figures or significant digits. - The larger the number of significant figures obtained in a measurement, the greater is the accuracy of the measurement. The reverse is also true.
- If one uses the instrument of the smallest least count, the number of significant digits increases.
Rules for determining significant figures:
- All the non-zero digits are significant; for example, if the volume of an object is 178.43 cm3, there are five significant digits, which are 1, 7, 8, 4, and 3.
- All the zeros between two nonzero digits are significant; e.g., m = 165.02 g has 5 significant digits.
- If the number is less than 1, the zero/zeroes on the right of the decimal point and to the left of the first nonzero digit are not significant, e.g., in 0.001405, the underlined zeroes are not significant. Thus the above number has four significant digits.
- The zeroes on the right-hand side of the last nonzero number are significant (but for this, the number must be written with a decimal point), e.g., 1.500 or 0.01500 both have 4 significant figures each.
On the contrary, if a measurement yields length L given as L = 125 m = 12500 cm = 125000 mm, it has only three significant digits.
उत्तर २
- Significant figures are those meaningful digits that are known with certainty.
- They indicate uncertainty in an experiment or calculated value. For example, if 15.6 mL is the result of an experiment, then 15 is certain while 6 is uncertain, and the total number of significant figures is 3.
-
Hence, significant figures are defined as the total number of digits in a number, including the last digit that represents the uncertainty of the result.
Notes
Students should refer to the answer according to their questions.
संबंधित प्रश्न
What do you mean by significant figures?
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:
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?
5 × 5.364
How many significant figures should be present in the answer of the following calculation?
0.0125 + 0.7864 + 0.0215
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?
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 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.
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?
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).
It is a well known fact that during a total solar eclipse the disk of the moon almost completely covers the disk of the Sun. From this fact and from the information you can gather from examples 2.3 and 2.4, determine the approximate diameter of the moon.
State the number of significant figures in the following:
6.032 N m–2
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.
Answer the following question.
Describe what is meant by order of magnitude.
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.
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 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 ______.
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 ______.
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 ______.
Significant figures in a measurement include which of the following?
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?
What is the least count of a measuring instrument?
How many significant figures are there in the number 0.001405?
Which of the following numbers has 4 significant figures?
The radius of Earth is expressed as 0.64 × 10⁷ m in scientific notation. What is its order of magnitude and number of significant figures?
