SDcientific Notation & Rounding off - Units & Measurements Video Lecture - Class 11

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before going ahead with part 9 notation
that is called the scientific notation
so we started representing numbers in
terms of scientific notation so that
even if the units are changed the number
of significant figures remains the same
so what is scientific notation in
scientific notation each number is
represented in the form of a into 10 to
the power P where P is the power which
is just any integer and the coefficient
that is a is called significant so the
terminology used or a is significant we
will take an example now let us consider
this example how can we write this
number in scientific notation we can
write it as 5 into 10 to the power 3 so
this Q is an integer and this 5 is the
significant now what you could be right
as the power of 10 they will never be
considered for significant figures so
the number of significant figures will
be counted with this number
cactus wrestling again let us take
another example so zero point zero zero
zero zero zero seven six now how do you
write it in scientific notation we write
it seven point six one two three four
five six so 10 to the power minus 6 now
this will not be considered
I'm counting this number of significant
figures so here the number of
significant figures would be 1/2 that is
2 so we start writing all the numbers
uniformly in scientific notation there
is no discrepancy which arises when we
change the units now that we came to
know what the scientific notation let us
take an example to see how it overcomes
the ambiguity which will seems to
revisit with the significant figures
suppose we have a length which is
measured as seven point six meters so
how many significant figures are there
true now suppose we can put we want to
convert it into centimeters so that
would become seven point 6 into 10 to
the power 2 centimeters so again this
would have to live in figures this when
converted into kilometers would be 7
point 6 into 10 to the power minus 3
kilometers so again this 1/2 this could
have 2 so that means by conversion of
units the only thing that will keep
changing is this thing and not the
significant they are good from the
significant the number of significant
digits will remain the same there are a
certain rules to be followed for
arithmetic operations with significant
figures rule number one in
multiplication or division the final
result should look in as many
significant figures as are there in
original number with the least
significant figures that means let us
suppose we are multiplying two
multiplying or dividing two or more
numbers each of them have different
number of significant figures in that
case the result will have the number of
significant figures as many
as present in the one which are the
least significant figures for example
let us say we multiplying five point
eight seven nine with four point six
five how many significant figures are
there in this case it has four
significant figures in this case it has
three significant figures now when we
get the result it comes out to be
something like this so how should we
represent the figure how many
significant digits should be there the
number of significant this is four and
this is three so three is the least one
so the result should have three
significant figures so we have twenty
seven point three as the answer
similarly rule number two it states in
addition or subtraction the final result
should retain as many decimal places as
are there in the number with then we use
two decimal places it is exactly the
same as in terms of multiplication or
division that is in this case in this
case we talked about significant figures
in this case we are talking about the
decimal places here let us suppose we
are multiplying six point we are adding
this zero is by error so let us suppose
we are item 6.1 - one plus seven point
four plus eight point one two three so
how many decimal places are there in
this case decimal places three in number
of decimal places this one here the
number of decimal places is three so how
many decimal places that answer should
have it should have one decimal place
that is the result should be twenty one
point six so in case of multiplication
or division the result should have as
many significant figures as there are
with the number which has least
and figures and in case of addition or
subtraction we don't talk of significant
figures we talk of the number of decimal
places so during multiplication and
division we talk of significant figures
in case of addition and subtraction we
talk of the number of decimal places I
go with a clear till now now we will
learn how to round or uncertain digit I
already told you whenever we say talk of
any number say four point eight nine new
movie in this case for age nine - they
are all considered to be reliable digits
and the last one is considered to be the
uncertainty juice now at many times we
want to round off the uncertainty juice
so what is the procedure for rounding
off there are two things which we do -
rounding up and the other is rounding
down so let us see rounding up in case
of rounding up we increase the
terminating digit by one and drop off
the digits to the right if the digit is
greater than five
let us suppose we have an example five
point four seven five seven in this case
if we want it if we want to round off
this number to tree decimal places at
present the number has four decimal
places
suppose I want to round it off to three
decimal places what would it be when I
want to round a dog since 7 is greater
than 5
the last digit so that means I want to
remove one digit so we will see the
digit which we want to remove if that
digit is greater than five in that case
we will increase this digit by one and
choose this digit
that is we can write it as five point
four seven six
now suppose if I want to round up the
digit to two decimal places in that case
I want to remove these two digits
correct so in that case we will check
for the second digit now say I want to
round this digit to one decimal place
now this was the case for Chile decimal
places now suppose I want to round it
all to one decimal place for one decimal
place we want to remove all the digits
from here so this seven is again greater
than five so what we will do we will
increase four by one and we will remove
all the other digits so we will write it
as five point five so that is rounding
up now when we talk about in down what
we do is similarly in this case suppose
then we have a digit five point four
seven five two now I want to round this
digit off to three decimal places I want
to round it off up to three decimal
places that means I want to remove this
digit this digit is less than five so
what I do is I just remove this digit
and leave everything else as it is so I
write it as four five point four seven
five correct so this is how we round up
and round down so first we need to check
how many digits we want to round it up
or down get down if the digit is greater
than five we increase the previous digit
by one and then remove that digit if the
digit is less than five then we leave
the previous digit as it is just remove
that it motels the terminating digit is
equal to five when
in that case we will again have two
different scenarios let us suppose that
we have some digit say two point three
five four now we want to round it off to
one decimal place that means we want to
remove these two digits now here you see
that this digit is equal to five it is
neither greater than nor less than five
so in this case what we look for is
whether this digit is even or odd
if this digit is odd in this case we
will increase this digit by 1 so we will
write it as 2.4 in case that is this
scenario that is if the digit is odd so
we write it as 2.4
now if the preceding digit is even for
example if we had it to 1 2 5 foot in
this case this is 5 and this is an even
number so in this case we could have
written it as 2.2 so I think it is clear
now so rounding off will have two
categories rounding up and rounding down
we will round up when the terminating
digit is greater than 5 we will round
down when the terminating digit is less
than 5 when the terminating digit is
equal to 5 in that case if the preceding
digit is even we will leave it as it is
if the preceding digit is odd we will
increase it by 1 let us look at an
example problem the problem asks
calculate the surface area of a cube
where each side measures 7 point 2 0 3
meters now surface area of a cube is
equal to
six into side square so here it would be
6 into 7 point 2 0 3 into 7 point 2 0 3
so this comes out to be 3 1 1 point 2 9
9 2 5 4 meter square now we have to
round it off so to how many digits will
belong to top as we discussed in a rule
that in case of multiplication the least
number of significant digit whatever
number of decimal places we have in the
site we will try to round you talk to
that many digits so we will round it up
till 3 1 1 point 3 meter square that is
after 2 we have 9 which is greater than
5 so we will increase 2 by 1 and we will
remove all the digits from here so it
will be 3 1 1 point 3 meter square thank
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