Rules to Compare Numbers Video Lecture - Class 6

hello friends this video on
understanding numbers part 4 is brought
to you by exam feel calm no more fear
from exam now when we have to deal with
such bigger numbers now it is very
important that we know the position of
each digit in a number so there are
different places in a number so let us
start with a smaller number at twenty
five so in twenty five five is at the
unit's place and two is at the tens
place now why do I call this a unit's
place
and why do I call the tens place now how
can we write 25 we can say this is 2
into 10 plus 5 into 1 so basically 5 x 1
to x 10 y is 2 multiplied by 10 because
2 is at the tens place right and that is
why you get it as 25 so basically the
last digit the corner most digit is
always at the unit's place the next
digit is at the tens place the next
digit here would be at the hundreds
place thousands place ten thousand
plates and so on so this is the sequence
of the positions of digits units tens
hundreds thousands ten thousands one
lakh ten lakh and so on so let us look
at another example like four five six
that is 456 so this would be units place
this would be tens place and this would
be hundreds place so how can we write
this we will write it as 4 into hundred
plus 5 into 10 plus 6 into 1 so how much
will you get out of this you get 456
let's look at more examples so here you
have a five digit number so this would
be units tens hundreds thousands ten
thousands so basically this can be
written as two so let us start from unit
space so this would be 2
- one next is 5 that is tens place so
that would be 5 into 10 next is 0 which
is at 100 space so this would be 0 in
200 next is 7 which is at thousand place
so this would be 7 in 2002 that you have
- which is at n thousands place so this
would be 2 into 10,000 so this is how
you get 27,000 50 - yet big enough
number so this would be unit 10 100
thousands ten thousands one lakh right
and similarly if if you have even bigger
numbers so the position will continue in
this fashion so these are the positions
now why did I talk about the position
that's because now when we talk about
bigger number smaller number we will
talk about a lot of other things so that
time when you know this concept of
positioning of the digits it will be
easier for you to understand so now
without is wasting any further time let
us quickly look at the rules to compare
numbers how do we know which number is
bigger and which number is smaller so
there are a few rules to remember rule
number one a number with more number of
digits is always greater so for example
you have a digit like this 2 6 5 9 4 3 2
and you have another number like this 4
3 9 8 2 4 3 9 6 8 5 9 1 for 2 now
looking at these two numbers if I
instantly ask you which is greater so
the number with greater number of digits
so this number has more number of digits
it has 1 2 3 4 5 6 7 8 9 10 11 so this
is an eleven digit number whereas this
one is a seven digit number so
definitely this number is greater than
this number so this is rule number one
so if you have to compare two numbers
with different number of digits the one
with greater
number of digits is a greater number
rule number 2 a number with digits in
descending order is the greatest number
possible with those digits now this is
something that we had discussed in one
of the previous slides that let us
suppose if you have some digits like 5 9
2 1 6 5 4 2 so if you are given a set of
digits now in for these set of digits
the greatest number would be the one
where the digits are ordered in
descending order that is in decreasing
order so the number should start with
the greatest digit which is 9 then
should come the next digit to just 6
then should come the next digit that is
fine and so on and you order all the
digits in descending order you get the
greatest number that is possible with
these digits
similarly a number with digits in
ascending order is the smallest number
possible with those digits so for these
digits the smallest number would start
with 1 then 2 and then 4 5 6 9 and so on
so these are some simple rules with the
help of which we can compare bigger
numbers so let us compare a few numbers
1 4 6 7 & 6 1 7 8 0 which is greater
obviously 6 1 7 8 0 because it has 5
digits and this has 4 digits so this is
bigger 1 4 6 7 & 6 1 7 8
now here both the numbers have the same
number of digits so which one is greater
now here look at the first digit here
the first digit is 1 and here the first
digit is 6 so 6 is greater than 1
therefore this is a bigger number right
now why are we comparing this number the
first number because this first number
is at the thousands place right this is
units tens hundreds thousand so one at
the thousand
means that this number is in the range
of 1000 and here six is in the thousands
place that means this number is in the
range of 6,000 so which is definitely
bigger
so therefore this number is greater than
this number one four six seven and the
zero six one seven eight right here this
is an interesting patch now you might
say that this is a four digit number
this is a five digit number so this
should be greater but that is not the
case because in this number the first
digit is a zero and whenever you have a
zero at the beginning of the number that
zero doesn't have any value so basically
zero six one seven eight is same as six
one seven eight do you want me to prove
that that how zero six one seven eight
is equal to six one seven eight now let
us try to expand six one seven eight so
we can expand it somewhat like this
sixes at the thousands place so six into
thousand plus one in two hundred plus 7
into 10 plus 8 into one so this is how
we can expand six one seven eight now
what about zero six one seven eight how
can we expand this this would be
something like this zero into 10,000
plus 600,000 plus one in two hundred
plus 7 into 10 plus 8 into 1 so this is
how we expand this but here in this case
zero multiplied by ten thousand zero
multiplied by anything becomes zero so
basically this term becomes 0 so you are
left with the same thing as you had in
this case and that is why we say that
whenever you have zero as the first
digit of the number that 0 doesn't have
any value because this term vanishes
altogether so here also it actually
means one four six seven and six one
seven eight but anyways six one seven
eight is greater than one two six seven
that is a different story but what I am
trying to say is just by looking at the
number of digits you cannot see
this is greater let's look at another
example 1 1 1 and 1 1 1 1 1 so here you
have just one digit being repeated
number of times so in this case it is
repeated 3 times where it is repeated 5
times here it has more number of digits
so this is a bigger number so in this
fashion you can compare number so even
if you are given larger numbers you can
follow these rules you can look at the
position of the digits and you can
decide which one is bigger and which one
is smaller now let us look at this
scenario here we see that this girl she
has a book and the cost of the book is
rupees 150 for this other girl let's
name her laka salata is this girl and
this girl let's call her Seema
so Seema has her book and the cost of
the book is rupees 1 554 that is rupees
1 5 4
now letter doesn't have this book and
she also wants to buy this book but the
amount of money that she has is 145 and
the cost of the book is 154 now with
rupees 145 in her wallet do you think
that Lata would be able to buy this book
no why
that's because 145 is lesser than 150 so
145 is less than 154
some of you might think that 145 and 154
both these numbers they contain the same
digits so both the numbers are made up
of three digits 1 4 and 5 but what
happened
shifting the digits change to the number
as a whole that that's what we had
learned before also that the moment you
change the position of the digits that
overall the number changes now here if
you look at 145
so here 5 is at units place for is at
space and one is at hundreds please so
it is basically one in 200 plus 4 into
10 plus 5 into 1 but in this case what
happens 5 + 4 gets interchanged
so here 4 is at units please 5 bills at
tens place and one is at hundreds place
so this is 1 in 200 plus 5 into 10 plus
4 into 1 so the value of this part
changes in both of them and that is why
the overall the number changes so what
we learn is shifting digits can change
the number in fact in most of the cases
as long as we are not talking about
repetitive digits let's say instead of 1
4 5
had it been 1 1 5 so if you interchange
the position of both the ones so that
might not matter but as long as you have
unique numbers and if you need digits
and if you shift those digits the number
will get changed
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