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Rule 4 : The “even” preceding digit (uncertain digit of the significant figures) is left unchanged, if the digit following it is 5. For example, a value of 2.525 is rounded as “2.52” to have three significant figures or to have two decimal places.

Rule 5 : If mathematical operation involves intermediate steps, then we retain one digit more than as specified by the rules of mathematical operation. We do not carry out “rounding off” in the intermediate steps, but only to the final result.

Rule 6 : In the case of physical constants, like value of speed of light, gravitational constant etc. or in the case of mathematical constants like “π”, we take values with the precision of the operand having maximum precision i.e. maximum significant numbers or maximum decimal places. Hence, depending on the requirement in hand, the speed of light having value of “299792458 m/s” can be written as :

c = 3 X 10 8 m / s 1 significant number

c = 3.0 X 10 8 m / s 2 significant number

c = 3.00 X 10 8 m / s 3 significant number

c = 2.998 X 10 8 m / s 4 significant number

Note that digit "9" appearing in the value is rounded off in the first three examples. In fourth, the digit "7" is rounded to "8".

Scientific notation

Scientific notation uses representation in terms of powers of 10. The representation follows the simple construct as given here :

x = a 10 b

where “a” falls between “1” and “10” and “b” is positive or negative integer. The range of “a” as specified ensures that there is only one digit to the left of decimal. For example, the value of 1 standard atmospheric pressure is :

1 a t m = 1.013 X 10 6 Pascal

Similarly, mass of earth in scientific notation is :

M = 5.98 X 10 24 K g

Order of magnitude

We come across values of quantities and constants, which ranges from very small to very large. It is not always possible to remember significant figures of so many quantities. At the same time we need to have a general appreciation of the values involved. For example, consider the statement that dimension of hydrogen atom has a magnitude of the order of “-10”. This means that diameter of hydrogen atom is approximately "10" raised to the power of "-10" i.e. 10 - 10 .

d 10 - 10

Scientific notation helps to estimate order of magnitude in a consistent manner, if we follow certain rule. Using scientific notation, we have :

x = a 10 b

We follow the rule as given here : If “a” is less than or equal to “5”, then we reduce the value of "a" to “1”. If “a” is greater than “5” and less than “10”, then we increase the value of “a” to "10".

In order to understand the operation, let us compare the order of magnitude of the diameter of a hydrogen atom and Sun. The diameters of Sun is :

d S = 6.96 X 10 8 m

Following the rule, approximate size of the sun is :

d s = 10 X 10 8 = 10 9 m

Thus, order of magnitude of Sun is “9”. On the other hand, the order of magnitude of hydrogen atom as given earlier is “-10”. The ratio of two sizes is about equal to the difference of two orders of magnitude. This ratio can be obtained by deducting smaller order from bigger order. For example, the relative order of magnitude of sun with respect to hydrogen atom, therefore, is 9 – (-10) = 19.

This means that diameter of sun is about 10 19 greater than that of a hydrogen atom. In general, we should have some idea of the order of magnitudes of natural entities like particle, atom, planets and stars with respect to basic quantities like length, mass and time.

Questions & Answers

what is phylogeny
Odigie Reply
evolutionary history and relationship of an organism or group of organisms
AI-Robot
ok
Deng
what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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