Table of contents |
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Introduction |
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Scientific Notation |
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What are Significant Figures? |
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Multiplication and Division |
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Order of Magnitude |
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Rounding |
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There are effective methods for managing numbers and presenting data in a clear and accurate way, such as:
Scientific Notation
Example: We can write 232.508 as 2.32508 × 102 in scientific notation. Similarly, 0.00016 can be written as 1.6 × 10–4.
Thus, we can write 232.508 as 2.32508 × 102 in scientific notation. 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 103
(b) 208 = 3
(c) 5000 = 5.0 x 103
(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 10n here N is termed as
(a) non –digit term
(b) digit term
(c) numeral
(d) base term
Ans: (b)
Solution:
In exponential notation N × 10n, N is a number called digit term which varies between 1.000 and 9.000….
Using the second ruler, it’s possible to estimate that the leaf is 3.52 cm long, but it is not possible to measure that accurately with the first ruler. In this way, the number of digits in the measured value gives us an idea of the maximum accuracy of the measurement. These are called significant digits or significant figures.
When it comes to calculations involving significant figures, the approach differs depending on whether you're adding, subtracting, multiplying, or dividing. Let's focus on addition and subtraction first.
Rule for Addition and Subtraction:
Limit the final answer to the rightmost column where all the numbers being added or subtracted have significant figures.
Example: Adding 1.2 and 4.71
Since 1.2 is the limiting factor, we round the final answer to the tenths column.
Rounding Rule:
Round up if the first dropped digit is 5 or greater, and round down if it is less than 5.
When multiplying or dividing numbers, it's important to consider the number of significant figures in each number. The final answer should have the same number of significant figures as the number with the fewest significant figures.
Example:
Example 2:
Scientific notation is a helpful method to express significant figures clearly:
Scientific notation ensures that all significant figures are clearly represented.
Example: Let's look at some examples to understand the order of magnitude better:
(a) 49 can be written as 4.9 × 10 1 , so the order of magnitude is 1.
(b) 51 is 5.1 × 10 1 , which gives an order of magnitude of 2.
(c) 0.049 is 4.9 × 10 -2 , so the order is -2.
(d) 0.050 is 5.0 × 10 -2 , leading to an order of -1.
(e) 0.051 is 5.1 × 10 -2 , resulting in an order of -1 as well.
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.
Example: 5.677, rounded to three significant digits, is 5.68
Example: 561200, rounded to three significant digits, is 561000
Example: 45850, rounded to three significant digits, is 45800
Example: 3.47588, rounded to three significant digits, is 3.48
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.
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1. What is scientific notation and why is it used? | ![]() |
2. How do I determine the number of significant figures in a measurement? | ![]() |
3. How do I apply significant figures when multiplying or dividing? | ![]() |
4. What is order of magnitude and how is it calculated? | ![]() |
5. How do I properly round numbers in scientific notation? | ![]() |