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Examples: Number systems and Expansion Video Lecture - CTET & State TET
FAQs on Examples: Number systems and Expansion Video Lecture - CTET & State TET
| 1. What are number systems and why are they important? |  |
Answer 1. Number systems are a way to represent and express numbers using a set of symbols or digits. They are important because they allow us to perform mathematical operations, communicate quantities, and solve problems in various fields such as science, engineering, and finance.
| 2. How many types of number systems are there? | |
Answer 2. There are several types of number systems, including the decimal system (base-10), binary system (base-2), octal system (base-8), and hexadecimal system (base-16). These are the most commonly used number systems, but there are others as well.
| 3. What is the decimal number system? | |
Answer 3. The decimal number system, also known as the base-10 system, is the most widely used number system. It uses ten digits (0-9) to represent numbers. Each digit's place value is determined by its position in the number, with the rightmost digit being the ones place, the next digit to its left being the tens place, and so on.
| 4. How does the binary number system work? | |
Answer 4. The binary number system, also known as the base-2 system, uses only two digits: 0 and 1. It represents numbers by using powers of 2. Each digit's place value is determined by its position in the number, with the rightmost digit being the ones place (2^0), the next digit to its left being the twos place (2^1), and so on.
| 5. How can number systems be expanded beyond their base? | |
Answer 5. Number systems can be expanded beyond their base by introducing additional symbols or digits. For example, the hexadecimal system (base-16) uses the digits 0-9 for numbers 0-9, and letters A-F for numbers 10-15. This allows for a larger range of numbers to be represented using a limited set of symbols.
Text Transcript from Video
hello friends this video on
understanding numbers path eight is
brought to you by exam feel calm no more
fear from exam so now be used on
whatever we have studied so far that is
trying to attempt a few question
question number one fill in the blanks
question number one fill in the blanks
one lakh is equal to - ten thousands so
how many ten thousands make one lakh so
let us quickly remember the positions of
various digits in a number it starts
with units tens hundreds thousands ten
thousands one lakh ten lakh and so on
now if for every one John there is a ten
involved right for every one John so for
ten thousand to one lakh so one that is
a bigger number so one that would be
equal to ten ten thousand 1 million is
equal to - 100 thousands now just now we
had learned that what is 1 million 1
million is nothing but 10 lakhs right
and what is 10 lakhs 10 lakhs is 1 lakh
is basically 100 thousand how do we
write 1 lakh 1 lakh is this so this is 1
lakh and this is how we write 100,000 so
this is also called 100,000 it is just
that this is Indian system of numeration
and this is the international system so
basically 1 million is equal to 10 lakhs
that means 1 million is equal to ten
hundred thousands because one lakh is
100,000 so this would be 10 1 crore is
equal to - 10 lakhs so and again you
remember this after 10 lakhs
one clove so again one crore and 10
lakhs they again have just one jump in
between so this would be 10 10 lakhs
1 crore is equal to - million okay let's
come back to million so million 1
million is equal to 10 lakhs so 1
million is 10 lakhs and that is what we
have to write so 1 million is equal to
10 lakhs and what about 1 crore is equal
to how many millions so when it comes to
1 crore 1 crore is again equal to 10
lakhs right looking at this you can say
that 1 crore is equal to 10 lakhs and 10
lakhs is equal to 1 billion right so 10
grows
what so 1 crore which actually mean 10
million right while looking at this and
this so here you see 1 crore is equal to
10 10 lakhs and 10 lakhs is equal to 1
million so that means this 10 lakh can
be replaced with 1 billion so you are
left with 10 million so 1 crore is equal
to 10 billion so please understand these
concepts so the only thing that you need
to remember is 1 is this positioning
should be remembered and every time you
are moving from right to left for every
one jump
you just keep my decline 10 that's
pretty simple and when it comes to
million just remember that 1 million is
equal to 10 lakhs everything else you
can derive from this question number 2
please form as correctly and write the
numerals so the first one is 73 lakh 75
thousand 307 so how do we write this so
let us start writing it from the UNIX
please so let's say this is unit tens
hundreds thousands ten thousands lakhs
10 lakhs
close 10 close and so on so now for the
first 173 lakhs so where should this be
placed in the labs so it is 73 lakhs
75,000 75,000 in thousands pays 307 307
now if you have to place the Commons
correctly where should you place the
commas
so the commas should separate the lakhs
and the thousands from each other so one
come after the lakhs while a comma after
the thousands and that's how we have
written it in numeral let's look at the
next one 9 crore 5 lakh 41 so now in
clove I will scroll the scroll so 9
kroll 5 lakh so 5 lakh so here it is
what would be in the 10 lakh please this
is going to be 0 because it is only 5
lakh so this would be 0 5 and 41 so 41
would be in the tens and units please
right so what about the thousands please
they are going to be 0 the hundreds
place is also going to be 0 now when you
have to place the commas where will you
put the commas they should separate the
close lakhs and the thousands so this is
how you advance the commas so let's have
a look at the third one 77 crore 52 lakh
twenty one thousand three hundred
two so 7 crore so again this would be
here and the crows place 52 lakhs so
this would come here 52 lakhs
twenty-one thousand would be here 302 so
this would be here so this was pretty
Singh but now that we have done the
first two the third one seems simple
let's move ahead with the fourth one
58 million four hundred twenty three
thousand two hundred two now here
looking at this million you can
distinguished that it is not following
the Indian system it is following the
international system so in international
system how would the placing would be it
would be units tens hundreds thousands
ten thousands but instead of lab you
will have 100 thousand then you will
have 1 million then you will have tip
million then you will have hundred
million so this would be different in
the international system so now we will
consider this international system
it sees 58 million so this 58 million
would come in the millions each long the
minions change you have three things
hundred million 10 million 1 million so
this would fall in the range of 10
million because you have 50 to 58
million so the 5 would be here the 8
would be here so this would make it 58
million four hundred twenty-three
thousand that is for twenty-three
thousand so here we again thousands we
have three places like so what are those
three pieces that would be covered
423,000 so this would be four hundred
twenty-three thousands so all the three
thousand space has been covered and then
the last two hundred two so this would
be two hundred two so this becomes fifty
eight millions for twenty-three
thousands and two hundred - right okay
now let's look at the last one which
says 23 lakhs
thirty thousand ten twenty three lakhs
again from here 23 lakhs thirty thousand
and ten so ten would be in the tens and
units please so the hundreds place will
have a zero so this is 23 lakh thirty
thousand ten so basically available you
have to write in numerals first you
write down the positioning of the digits
unit chains and rugs houses etc now
depending on whether it is the Indian
system or the international system you
write the positioning accordingly and
then just reading the name you start
putting the digits at appropriate places
question number three insert command
suitably and write the names according
to Indian system of numeration okay so
the first one so it's a a digit number
so how do we place the commas
appropriately now even before we place
the commas appropriately first letters
position the digits correctly so here we
have eight seven five nine five seven
six two so this is the units tens
hundreds thousands ten thousands lakhs
10 lakhs close so this is the position
now can you place the commas correctly
so we have to separate the clothes from
lags and the lags from the thousands and
the thousands from the rest of them so
let's separate the clothes
then let's separate the lakhs then rest
then let's separate the thousands so we
have placed the commas correctly so now
it's very easy for you to write it it is
8 crores
75 lakhs
95,000
762
you
let's look at the second one it says
eight five four six two eight three so
let's again position the digits units
tens hundreds thousands ten thousands
lakhs 10 lakhs so this is the smaller
digit as compared to the first one so
let's separate the top lakhs and the
thousands and that's how we have placed
the commas so this would be eighty five
flags forty six thousands 283 so this is
how we can name numerals doesn't matter
how big they are if we are able to
position the digits correctly then we
will be able to do it appropriately
question number four insert commas
suitably and write the names according
to the international system of
numeration let's get started with the
first one it is seven eight nine two one
zero nine - so this is units tens
hundreds thousands ten thousands hundred
thousands millions ten millions right
because we are following the
international system now so what it
would be let's separate the millions
then let's separate the thousands and
then we have the rest of it so from this
we see that it is 78 million and
20 1092 so this would be 78 millions 92
921 thousands and 92
let's look at the next one
it is 7 4 5 2 2 8 3 so this is units
tens hundreds thousands ten thousands
hundred thousands billion so let's
separate the millions and the thousands
so this becomes 7 million four hundred
fifty mm because all these three four
hundred thousands so 452 thousands
283 so this is how we named it as for
the international system of numeration
thank you please visit exam fee or come
for free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
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biology along with practical videos so
please subscribe to our channel for
daily updates thank you
understanding numbers path eight is
brought to you by exam feel calm no more
fear from exam so now be used on
whatever we have studied so far that is
trying to attempt a few question
question number one fill in the blanks
question number one fill in the blanks
one lakh is equal to - ten thousands so
how many ten thousands make one lakh so
let us quickly remember the positions of
various digits in a number it starts
with units tens hundreds thousands ten
thousands one lakh ten lakh and so on
now if for every one John there is a ten
involved right for every one John so for
ten thousand to one lakh so one that is
a bigger number so one that would be
equal to ten ten thousand 1 million is
equal to - 100 thousands now just now we
had learned that what is 1 million 1
million is nothing but 10 lakhs right
and what is 10 lakhs 10 lakhs is 1 lakh
is basically 100 thousand how do we
write 1 lakh 1 lakh is this so this is 1
lakh and this is how we write 100,000 so
this is also called 100,000 it is just
that this is Indian system of numeration
and this is the international system so
basically 1 million is equal to 10 lakhs
that means 1 million is equal to ten
hundred thousands because one lakh is
100,000 so this would be 10 1 crore is
equal to - 10 lakhs so and again you
remember this after 10 lakhs
one clove so again one crore and 10
lakhs they again have just one jump in
between so this would be 10 10 lakhs
1 crore is equal to - million okay let's
come back to million so million 1
million is equal to 10 lakhs so 1
million is 10 lakhs and that is what we
have to write so 1 million is equal to
10 lakhs and what about 1 crore is equal
to how many millions so when it comes to
1 crore 1 crore is again equal to 10
lakhs right looking at this you can say
that 1 crore is equal to 10 lakhs and 10
lakhs is equal to 1 billion right so 10
grows
what so 1 crore which actually mean 10
million right while looking at this and
this so here you see 1 crore is equal to
10 10 lakhs and 10 lakhs is equal to 1
million so that means this 10 lakh can
be replaced with 1 billion so you are
left with 10 million so 1 crore is equal
to 10 billion so please understand these
concepts so the only thing that you need
to remember is 1 is this positioning
should be remembered and every time you
are moving from right to left for every
one jump
you just keep my decline 10 that's
pretty simple and when it comes to
million just remember that 1 million is
equal to 10 lakhs everything else you
can derive from this question number 2
please form as correctly and write the
numerals so the first one is 73 lakh 75
thousand 307 so how do we write this so
let us start writing it from the UNIX
please so let's say this is unit tens
hundreds thousands ten thousands lakhs
10 lakhs
close 10 close and so on so now for the
first 173 lakhs so where should this be
placed in the labs so it is 73 lakhs
75,000 75,000 in thousands pays 307 307
now if you have to place the Commons
correctly where should you place the
commas
so the commas should separate the lakhs
and the thousands from each other so one
come after the lakhs while a comma after
the thousands and that's how we have
written it in numeral let's look at the
next one 9 crore 5 lakh 41 so now in
clove I will scroll the scroll so 9
kroll 5 lakh so 5 lakh so here it is
what would be in the 10 lakh please this
is going to be 0 because it is only 5
lakh so this would be 0 5 and 41 so 41
would be in the tens and units please
right so what about the thousands please
they are going to be 0 the hundreds
place is also going to be 0 now when you
have to place the commas where will you
put the commas they should separate the
close lakhs and the thousands so this is
how you advance the commas so let's have
a look at the third one 77 crore 52 lakh
twenty one thousand three hundred
two so 7 crore so again this would be
here and the crows place 52 lakhs so
this would come here 52 lakhs
twenty-one thousand would be here 302 so
this would be here so this was pretty
Singh but now that we have done the
first two the third one seems simple
let's move ahead with the fourth one
58 million four hundred twenty three
thousand two hundred two now here
looking at this million you can
distinguished that it is not following
the Indian system it is following the
international system so in international
system how would the placing would be it
would be units tens hundreds thousands
ten thousands but instead of lab you
will have 100 thousand then you will
have 1 million then you will have tip
million then you will have hundred
million so this would be different in
the international system so now we will
consider this international system
it sees 58 million so this 58 million
would come in the millions each long the
minions change you have three things
hundred million 10 million 1 million so
this would fall in the range of 10
million because you have 50 to 58
million so the 5 would be here the 8
would be here so this would make it 58
million four hundred twenty-three
thousand that is for twenty-three
thousand so here we again thousands we
have three places like so what are those
three pieces that would be covered
423,000 so this would be four hundred
twenty-three thousands so all the three
thousand space has been covered and then
the last two hundred two so this would
be two hundred two so this becomes fifty
eight millions for twenty-three
thousands and two hundred - right okay
now let's look at the last one which
says 23 lakhs
thirty thousand ten twenty three lakhs
again from here 23 lakhs thirty thousand
and ten so ten would be in the tens and
units please so the hundreds place will
have a zero so this is 23 lakh thirty
thousand ten so basically available you
have to write in numerals first you
write down the positioning of the digits
unit chains and rugs houses etc now
depending on whether it is the Indian
system or the international system you
write the positioning accordingly and
then just reading the name you start
putting the digits at appropriate places
question number three insert command
suitably and write the names according
to Indian system of numeration okay so
the first one so it's a a digit number
so how do we place the commas
appropriately now even before we place
the commas appropriately first letters
position the digits correctly so here we
have eight seven five nine five seven
six two so this is the units tens
hundreds thousands ten thousands lakhs
10 lakhs close so this is the position
now can you place the commas correctly
so we have to separate the clothes from
lags and the lags from the thousands and
the thousands from the rest of them so
let's separate the clothes
then let's separate the lakhs then rest
then let's separate the thousands so we
have placed the commas correctly so now
it's very easy for you to write it it is
8 crores
75 lakhs
95,000
762
you
let's look at the second one it says
eight five four six two eight three so
let's again position the digits units
tens hundreds thousands ten thousands
lakhs 10 lakhs so this is the smaller
digit as compared to the first one so
let's separate the top lakhs and the
thousands and that's how we have placed
the commas so this would be eighty five
flags forty six thousands 283 so this is
how we can name numerals doesn't matter
how big they are if we are able to
position the digits correctly then we
will be able to do it appropriately
question number four insert commas
suitably and write the names according
to the international system of
numeration let's get started with the
first one it is seven eight nine two one
zero nine - so this is units tens
hundreds thousands ten thousands hundred
thousands millions ten millions right
because we are following the
international system now so what it
would be let's separate the millions
then let's separate the thousands and
then we have the rest of it so from this
we see that it is 78 million and
20 1092 so this would be 78 millions 92
921 thousands and 92
let's look at the next one
it is 7 4 5 2 2 8 3 so this is units
tens hundreds thousands ten thousands
hundred thousands billion so let's
separate the millions and the thousands
so this becomes 7 million four hundred
fifty mm because all these three four
hundred thousands so 452 thousands
283 so this is how we named it as for
the international system of numeration
thank you please visit exam fee or come
for free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you
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Oct 15, 2025
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