Significant figures & Ambiguities - Units & Measurements Video Lecture - Class 11

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please make sure that you have watched
unit and measurement part 1 - part 7
before going ahead with part 8 we have
studied the different kinds of errors we
will study significant figures so what
do we mean by significant figures in any
number with decimal point and a large
number of digits following the decimal
point we say that all your reliable
digits plus the first uncertain digit
these two things together constitute the
significant figures let us take an
example let us say if we say a distance
as twenty four point five six seven
meters so how many significant figures
are there in this number all reliable
digits that is two four five and six
they are all new reliable digits and the
last digit that is the terminating digit
is all is the uncertain digit so here we
have two four five six as reliable
digits and seven as the uncertain digit
so the total number of significant
figures in this number is one two three
four and five so this number has five
significant figures let us say be saying
that your weight is forty five point
three kgs so how many significant
figures are there here the reliable
digits are 4 & 5 and 3 is the
digit there all we have three
significant figures there are the
certain rules which need to be followed
for defining significant figures so
we'll discuss each of the rules
the first rule all nonzero digits are
significant we write any number say we
write some we have something like forty
two point six nine four three two one
all are nonzero digits so they are all
significant so we have one two three
four five six seven eight we have eight
significant digits in this number
right second one all zeros between
nonzero digits are significant for
example let us suppose we have something
like four point zero nine to zero three
four so here we have zero between
nonzero digits like zero between four
and nine again zero between two and
three so these zeros are also
significant so even in this number how
many significant digits we have one two
three four five six seven so we have
seven significant digits in terminal
zeros without a decimal point are not
significant for example we consider any
number say four seven zero zero zero how
many significant digits are there in
this case the terminal zeros that means
there is no digit after the zero these
zeros and they do not have a decimal
point so these zeros are not considered
to be significant so if I ask you how
many significant digits are there in
this number there are only two
significant
because these zeros are not fast so
whenever you have zeros at the end and
there is no decimal point to join in
that is the zeros are not considered
significant keep a note of this point
again the terminal zeros with a decimal
point are significant so without a
decimal point is not significant but
with a decimal point is significant for
example we have something like four
point seven zero zero in this case if I
ask you how many significant digits are
there you have one two three four
because even though the zeros at the
terminal zeros but you have a decimal
point therefore in this case you have
four significant figures the next is for
example less than one zeros on the right
of decimal point but liftop first
non-zero digit are not significant let
us take an example which will make it
more clear suppose we have any number
which is less than one something like
this zero point zero one five four in
this case the zeros which are on the
right of the decimal point but left of
the first non-zero digit is first
non-zero digit is one
so if you consider this zero it lies
between 1 and it lies after the decimal
point so this zero will not be a
significant digit even this narrow will
not be a significant so in this is
we have just trees in so let us quickly
review the rules first is all nonzero
digits are significant second all zeros
between nonzero digits are significant
terminal zeros without a decimal point
are not significant but terminal zeros
with a decimal point are significant so
do not get confused with the third and
fourth point remember it when there is
no decimal point then the number is no
significant if there is a decimal point
then the number is significant so no
decimal point no significant decimal
point is there so at the significant so
whenever you have terminal zeros without
a decimal point
it is not significant whenever you have
terminal zeros with a decimal point they
are significant and the last one four
digits four numbers less than one their
zeros after the decimal point but before
the first non-zero digit they are also
considered not significant another point
to note here is change of units should
not change the number of significant
figures for example let us suppose we
have measured some length as forty three
point two centimeters so how many
significant digits are there one two
three they are all nonzero digits so
they are all significant so we have
three significant figures now if we
convert the same figure into some other
unit that is we converted it from
centimeters to meters so it became zero
point four three two meter in this case
this zero will not be
they're significant because it is before
the decimal point so again we have three
significant figures if we converted it
to kilometers it is zero point zero zero
zero four three two kilometers in this
case again this zero there not a
significant and these zeros will also
not be significant according to the
large screen because they are after the
decimal point but before the first
significant digit so even here the
number of significant figures between so
ideally whenever you change the unit the
number of significant figures should
remain unchanged however there are
certain ambiguities and significant
figures matters there are certain
contrary or controversial facts
regarding the significant figures we'll
seen that the ambiguities lie with the
terminal zeros rules for example the
rule say if the terminal zeros will
recall the rules quickly the two rules
will skip it says terminal zeros with
decimal point significant terminal zeros
no decimal point not significant so this
this was stated in the rules now we see
this example let us take this example
five point seven zero zero meters
according to the rules these are the
terminal zeros with a decimal point so
they should be significant so how many
significant because you have four now
you can put the same thing into
centimeter
you get five 17.0 centimeters in this
case again you have four significant
figures now you can put the same value
into millimeters and you get five seven
zero zero millimeters now in this case
there is no decimal point and you have
terminal zeros so these two zeros will
not be considered significant and the
number of significant figures will
reduce to two so this is an ambiguity
because we just now learned that the
change of units should not change the
number of significant figures so how to
resolve this contradiction to get rid of
this contradiction was developed another
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