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Some Basic Concepts of Chemistry - Uncertainty in Measurement (Scientific Notation, Significant Figures, Dimensional Analysis)

Grade 11CBSEChemistry

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Scientific Notation: Used to express very large or very small numbers in the form N×10nN \times 10^n, where 1≤N<101 \le N < 10 and nn is an exponent. For example, 0.00000160.0000016 is written as 1.6×10−61.6 \times 10^{-6}.

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Precision and Accuracy: Precision refers to the closeness of various measurements for the same quantity. Accuracy is the agreement of a particular value to the true value of the result.

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Significant Figures: The total number of digits in a number including the last digit whose value is uncertain. Rules: (1) All non-zero digits are significant. (2) Zeros between non-zero digits are significant. (3) Leading zeros are not significant. (4) Trailing zeros in a number with a decimal point are significant.

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Significant Figures in Calculations: In multiplication/division, the result must have the same number of significant figures as the measurement with the least significant figures. In addition/subtraction, the result should have the same number of decimal places as the term with the least decimal places.

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Dimensional Analysis (Factor Label Method): A method used to convert units from one system to another using conversion factors. A conversion factor is a ratio that equals 11, such as 1 m100 cm=1\frac{1 \text{ m}}{100 \text{ cm}} = 1.

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Rounding Off: If the digit to be removed is >5>5, the preceding digit is increased by 11. If it is <5<5, it is left unchanged. If it is exactly 55, the preceding digit is increased by 11 if it is odd, and left unchanged if it is even.

📐Formulae

N×10nN \times 10^n

Value in New Unit=Value in Old Unit×Conversion Factor\text{Value in New Unit} = \text{Value in Old Unit} \times \text{Conversion Factor}

Conversion Factor=Unit requiredUnit to be cancelled\text{Conversion Factor} = \frac{\text{Unit required}}{\text{Unit to be cancelled}}

💡Examples

Problem 1:

Add the following numbers taking significant figures into account: 12.1112.11, 18.018.0, and 1.0121.012.

Solution:

31.131.1

Explanation:

Performing vertical addition: 12.1118.00+1.01231.122\begin{array}{r} 12.11 \\ 18.0 \phantom{0} \\ + 1.012 \\ \hline 31.122 \end{array} Since the number 18.018.0 has only one digit after the decimal point (the least among all), the result must be rounded to one decimal place. Therefore, 31.12231.122 becomes 31.131.1.

Problem 2:

How many seconds are there in 22 days?

Solution:

1.728×105 s1.728 \times 10^5 \text{ s}

Explanation:

Using Dimensional Analysis: 1 day=24 h1 \text{ day} = 24 \text{ h}, 1 h=60 min1 \text{ h} = 60 \text{ min}, 1 min=60 s1 \text{ min} = 60 \text{ s}. Seconds=2 days×24 h1 day×60 min1 h×60 s1 min\text{Seconds} = 2 \text{ days} \times \frac{24 \text{ h}}{1 \text{ day}} \times \frac{60 \text{ min}}{1 \text{ h}} \times \frac{60 \text{ s}}{1 \text{ min}} Seconds=2×24×60×60 s=172800 s\text{Seconds} = 2 \times 24 \times 60 \times 60 \text{ s} = 172800 \text{ s} In scientific notation, this is 1.728×105 s1.728 \times 10^5 \text{ s}.

Problem 3:

Calculate the result of 2.5×1.250.5\frac{2.5 \times 1.25}{0.5} with correct significant figures.

Solution:

66

Explanation:

Calculated value: 2.5×1.250.5=6.25\frac{2.5 \times 1.25}{0.5} = 6.25. However, the numbers 2.52.5 and 0.50.5 have only 22 and 11 significant figures respectively. The result must be limited by the term with the fewest significant figures (0.50.5 has one significant figure). Thus, 6.256.25 is rounded to 66.