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Q.1 : What are significant figures, and why are they important in measurements?
Ans. Significant figures are digits in a numerical value that indicate the precision or certainty of a measurement. They are crucial because they convey the reliability and accuracy of a measurement, guiding scientists and engineers in making informed decisions based on data.
Q.2 : Can you provide an example of how significant figures are applied in real-life scenarios?
Ans. Imagine measuring the length of a table using a ruler with markings for every millimetre. The measurement might be recorded as 1.235 meters, indicating that the measurement is precise to the nearest millimetre and has four significant figures.
Q.3 : What is accuracy?
Ans. Accuracy refers to how close a measured value is to the true or accepted value. A measurement is considered accurate if it is close to the true value, indicating a small systematic error.
Q.4 : What is precision?
Ans. Precision refers to how close repeated measurements are to each other. A measurement is considered precise if repeated measurements yield similar results, indicating low random error or variability.
Q.5 : How do accuracy and precision differ?
Ans. Accuracy and precision are related but distinct concepts. Accuracy focuses on the closeness of measurements to the true value, while precision focuses on the closeness of measurements to each other, regardless of their closeness to the true value.
Q.6 : Can you provide an example to illustrate the difference between accuracy and precision?
Ans. Imagine a target with several arrows hitting close together but away from the bullseye. This scenario represents high precision but low accuracy. Conversely, if the arrows cluster tightly around the bullseye, this represents both high precision and high accuracy.
Significant Figures, Accuracy, Precision And Important Quantities, JEE 2025
Significant Figures : Understanding significant figures is crucial in chemistry for accurate measurements and data representation. Learn the rules for determining significant figures, handling zeros, and performing arithmetic operations to ensure precision in your chemical calculations and scientific reporting.
Shrivastav 5 Jun, 2024
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Significant Figures :
Welcome, curious learners, to the fascinating realm of scientific measurement! In the world of science, accurate and precise measurements are crucial for understanding the natural phenomena around us. To achieve this, scientists use concepts such as significant figures, accuracy, and precision. In this article, we'll explore these concepts in simple terms, along with some important quantities commonly encountered in science. By the end, you'll have a clearer understanding of how scientists ensure the reliability of their measurements and calculations.
What are Significant Figures?
Significant figures, also known as significant digits, are the digits in a number that contribute to its precision. They include all the certain digits plus one uncertain digit.
Why are Significant Figures Important?
Significant figures help convey the precision of a measurement or calculation. They indicate the degree of certainty in a number and guide scientists in expressing measurements accurately.
Rules for Determining the Number of Significant Figures:
All non-zero digits are significant. For example, 3.132 has four significant figures.
Zeros between two non-zero digits are significant. For example, 3.01 has three significant figures.
The zeros preceding to the first non-zero number (i.3. to the left of the first non-zero number) are not significant. Such zeros indicate the position of decimal point. For example, 0.324 has three significant figures.
All zeros at the end or to the right of a number are significant provided they are on the right side of the decimal point. For example, 0.0200 has three significant figures.
Exponential form: N × 10
n
. Where N shows the significant figure. E.g. 1.86 × 10
4
has three significant figure.
Rounding off the uncertain digit:
(i)
If the left most digit to be rounded off is more than 5, the preceding number is increased by one. E.g. 2.16 is rounded to 2.2.
(ii)
If the left most digit to be rounded off is less than 5, the preceding number is retained. Eg. 2.14 is rounded off to 2.1.
(iii)
If the left most digit to be rounded off is equal to 5, the preceding number is not changed if it is even the increased by one if it is odd. Eg., 3.25 is rounded off to 3.2. 2.35 is rounded off to 2.4.
What is Accuracy?
Accuracy refers to how close a measured value is to the true or accepted value. It indicates the absence of systematic errors in measurement.
What is Precision?
Precision refers to the consistency or reproducibility of a series of measurements. It indicates the degree of exactness or refinement in measurement.
Important Quantities:
Mass and Weight:
The mass of a substance is the amount of matter present in it while weight is the force exerted by gravity on an object. The mass of a substance is constant, whereas its weight may vary from one place to another due to changes in gravity. The SI unit of mass is the kilogram (kg). The SI-derived unit (unit derived from SI base units) of weight is Newton.
Volume :
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic meter.
Density :
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is (the lower case Greek letter rho). SI unit of density is kg m
–3
.
Temperature :
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. There are three common scales to measure temperature — °C (degree celsius), °F (degree fahrenheit) and K (kelvin). The temperature on two scales is related to each other by the following relationship:
°F = 9/5 (°C) + 32
K = °C + 273.15
Solved Examples Of significant figure
Q.1.
How many significant figure are there in each of the following numbers:
(i)
1.00 × 106
(ii)
0.00010
(iii)
π
Ans.
(i)
Three
(ii)
Two
(iii)
An infinite number
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