Many times in the study of chemistry, one has to deal with experimental data as well as theoretical calculations.
There are meaningful ways to handle the numbers conveniently and present the data realistically with certainty to the extent possible like:
Scientific Notation
Example: We can write 232.508 as 2.32508 × 10^{2} in scientific notation. Similarly, 0.00016 can be written as 1.6 × 10^{–4}.
Note that while writing it, the decimal had to be moved to the left by two places and the same is the exponent (2) of 10 in the scientific notation.
Similarly, 0.00016 can be written as 1.6 × 10^{–4}. Here the decimal has to be moved four places to the right and (– 4) is the exponent in the scientific notation.
Q.1. Which of the following options is not correct?
(a) 8008 = 8.008 x 10^{3}
(b) 208 = 0.208 x 10^{3}
(c) 5000 = 5.0 x 10^{3}
(d) 2.0034 = 4
Ans: (d)
Solution:
2.0034 = 4
Q.2. Exponential notation in which any number can be represented in the form, Nx 10^{n }here N is termed as
(a) non–digit term
(b) digit term
(c) numeral
(d) base term
Ans: (b)
Solution:
In exponential notation N × 10^{n}, N is a number called digit term which varies between 1.000 and 9.000….
Rules for Determining the Number of Significant Figures
(i) Addition And Subtraction of Significant Figures
The result cannot have more digits to the right of the decimal point than either of the original numbers.
12.11
18.0
1.012
31.122
Here, 18.0 has only one digit after the decimal point, and the result should be reported only up to one digit after the decimal point, which is 31.1.
(ii) Multiplication and Division of Significant Figures
The result must be reported in these operations with no more significant figures as in the measurement with the few significant figures.
2.5 × 1.25 = 3.125
Since 2.5 has two significant figures, the result should not have more than two significant figures. Thus, it is 3.1.
Q.1. How many significant figures are in each term?
(a) 34.6209 = 6
(b) 0.003048 = 4
(c) 5010.0 = 5
(d) 4032.090 = 7
Q.2. Solve the following equations using the correct number of significant figures.
(a) 34.683 + 58.930 + 68.35112 = 161.964
(b) 45001  56.355  78.44 = 44866
(c) 0.003 + 3.5198 + 0.0118 = 3.535
(d) 36.01  0.4  15 = 21
Q.3. Solve the following equations using the correct number of significant figures.
(a) 98.1 × 0.03 = 3
(b) 57 × 7.368 = 4.2 × 10^{2}
(c) 8.578/4.33821 = 1.977
(d) 6.90/2.8952 = 2.38
Q.4. How many significant figures are in each term?
(a) 1.40 × 10^{3} = 3
(b) 6.01 = 3
(c) 02947.1 = 5
(d) 583.02 = 5
When doing calculations using significant figures, you will find it necessary to round your answer to the nearest significant digit. There are therefore a few rules of rounding that help retain as much accuracy as possible in the final answer.
AMBIGUOUS ZEROS
So what happens if your calculation or measurement ends in a zero? For example, what if you measured a branch that was 200 cm (not 199 or 201 cm) long? The zeros in a measured value of 200 cm in this case appear ambiguous, since it could suggest that there is only one significant digit.
One way to reduce this ambiguity is to use significant figures with scientific notation.
Example: If the true value for a result is 2.00 g.
(a) Student ‘A’ takes two measurements and reports the results as 1.95 g and 1.93 g.
These values are precise as they are close to each other but are not accurate.
(b) Another student repeats the experiment and obtains 1.94 g and 2.05 g as the results for two measurements.
These observations are neither precise nor accurate.
(c) When a third student repeats these measurements and reports 2.01g and 1.99 g as the result.
These values are both precise and accurate.
Accuracy and Precision
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1. How is scientific notation used in mathematics and scientific fields? 
2. How do you perform multiplication and division with exponential numbers in scientific notation? 
3. Can you explain how addition and subtraction work with exponential numbers in scientific notation? 
4. What are significant figures and why are they important in scientific calculations? 
5. How do you round numbers when dealing with significant figures in scientific notation? 

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