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प्रश्न
Answer the following question.
Describe what is meant by significant figures.
What do you mean by significant figures?
उत्तर १
Significant figures:
- Significant figures in the measured value of a physical quantity is 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 smaller 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, eg., 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 can refer to the provided solutions based on their preferred marks.
संबंधित प्रश्न
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 126,000?
How many significant figures are present in the 2.0034?
Round up the following upto three significant figures:
10.4107
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
The relative density of lead is 11.3. Its density is ______ g cm–3or ______ kg m–3.
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?
You are given a thread and a metre scale. How will you estimate the diameter of the thread?
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.
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).
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:
0.007 m2
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.
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.
The radius of the circle is 3.12 m. Calculate the area of the circle with regard to 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`
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?
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 mass and volume of a body are 4.237 g and 2.5 cm3, respectively. The density of the material of the body in correct significant figures is ______.
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 ______.
