**Books**

We just looked at the number of digits and found the answer.
The greatest number has the most thousands and the smallest is
only in hundreds or in tens.
Make five more problems of this kind and give to your friends
to solve.
Now, how do we compare 4875 and 3542?
This is also not very difficult.These two numbers have the
same number of digits. They are both in thousands. But the digit
at the thousands place in 4875 is greater than that in 3542.
Therefore, 4875 is greater than 3542.
Next tell which is greater, 4875 or
4542? Here too the numbers have the
same number of digits. Further, the digits
at the thousands place are same in both.
What do we do then? We move to the
next digit, that is to the digit at the
hundreds place. The digit at the hundreds
place is greater in 4875 than in 4542.
Therefore, 4875 is greater than 4542.
1.2.2 Shifting digits
Have you thought what fun it would be if the digits in a number could shift
(move) from one place to the other?
Think about what would happen to 182. It could become as large as 821
and as small as 128. Try this with 391 as well.
Now think about this. Take any 3-digit number and exchange the digit at
the hundreds place with the digit at the ones place.
(a) Is the new number greater than the former one?
(b) Is the new number smaller than the former number?
Write the numbers formed in both ascending and descending order.
Before 7 9 5
Exchanging the 1st and the 3rd tiles.
After 5 9 7
If you exchange the 1st and the 3rd tiles (i.e. digits), in which case does the
number become greater? In which case does it become smaller?
Try this with a 4-digit number.
1.2.3 Introducing 10,000
We know that beyond 99 there is no 2-digit number. 99 is the greatest 2-digit
number. Similarly, the greatest 3-digit number is 999 and the greatest 4-digit
number is 9999. What shall we get if we add 1 to 9999?
Look at the pattern : 9 + 1 = 10 = 10 × 1
99 + 1 = 100 = 10 × 10
999 + 1 = 1000 = 10 × 100
We observe that
Greatest single digit number + 1 = smallest 2-digit number
Greatest 2-digit number + 1 = smallest 3-digit number
Greatest 3-digit number + 1 = smallest 4-digit number
MATHEMATICS
6
Should not we then expect that on adding 1 to the greatest 4-digit number,
we would get the smallest 5-digit number, that is 9999 + 1 = 10000.
The new number which comes next to 9999 is 10000. It is called
ten thousand. Further, we expect 10000 = 10 × 1000.
1.2.4 Revisiting place value
You have done this quite earlier, and you will certainly remember the expansion
of a 2-digit number like 78 as
78 = 70 + 8 = 7 × 10 + 8
Similarly, you will remember the expansion of a 3-digit number like 278 as
278 = 200 + 70 + 8 = 2 × 100 + 7 × 10 + 8
We say, here, 8 is at ones place, 7 is at tens place and 2 at hundreds place.
Later on we extended this idea to 4-digit numbers.
For example, the expansion of 5278 is
5278 = 5000 + 200 + 70 + 8
= 5 × 1000 + 2 × 100 + 7 × 10 + 8
Here, 8 is at ones place, 7 is at tens place, 2 is at hundreds place and 5 is at
thousands place.
With the number 10000 known to us, we may extend the idea further. We
may write 5-digit numbers like
45278 = 4 × 10000 + 5 × 1000 + 2 × 100 + 7 × 10 + 8
We say that here 8 is at ones place, 7 at tens place, 2 at hundreds place,
5 at thousands place and 4 at ten thousands place. The number is read as forty
five thousand, two hundred seventy eight.
1.2.5 Introducing 1,00,000
Which is the greatest 5-digit number?
Adding 1 to the greatest 5-digit number, should give the smallest
6-digit number : 99,999 + 1 = 1,00,000
This number is named one lakh. One lakh comes next to 99,999.
10 × 10,000 = 1,00,000
We may now write 6-digit numbers in the expanded form as
2,46,853 = 2 × 1,00,000 + 4 × 10,000 + 6 × 1,000 +
8 × 100 + 5 × 10 +3 × 1
This number has 3 at ones place, 5 at tens place, 8 at hundreds place, 6 at
thousands place, 4 at ten thousands place and 2 at lakh place. Its number
name is two lakh forty six thousand eight hundred fifty three.
1.2.6 Larger numbers
If we add one more to the greatest 6-digit number we get the smallest 7-digit
number. It is called ten lakh.
Write down the greatest 6-digit number and the smallest 7-digit number.
Write the greatest 7-digit number and the smallest 8-digit number. The smallest
8-digit number is called one crore.
Complete the pattern :
9 + 1 = 10
99 + 1 = 100
999 + 1 = _**
9,999 + 1 = _****
99,999 + 1 = _****
9,99,999 + 1 = _****
99,99,999 + 1 = 1,00,00,000
We come across large numbers in
many different situations.
For example, while the number of
children in your class would be a
2-digit number, the number of
children in your school would be
a 3 or 4-digit number.
The number of people in the nearby town would be much larger.
Is it a 5 or 6 or 7-digit number?
Do you know the number of people in your state?
How many digits would that number have?
What would be the number of grains in a sack full of wheat? A 5-digit number,
a 6-digit number or more?
Remember
1 hundred = 10 tens
1 thousand = 10 hundreds
= 100 tens
1 lakh = 100 thousands
= 1000 hundreds
1 crore = 100 lakhs
= 10,000 thousands
1.2.7 An aid in reading and writing large numbers
Try reading the following numbers :
(a) 279453 (b) 5035472
(c) 152700375 (d) 40350894
Was it difficult?
Did you find it difficult to keep track?
Sometimes it helps to use indicators to read and write large numbers.
Shagufta uses indicators which help her to read and write large numbers.
Her indicators are also useful in writing the expansion of numbers. For example,
she identifies the digits in ones place, tens place and hundreds place in 257 by
writing them under the tables O, T and H as
H T O Expansion
2 5 7 2 × 100 + 5 × 10 + 7 × 1
Similarly, for 2902,
Th H T O Expansion
2 9 0 2 2 × 1000 + 9 × 100 + 0 × 10 + 2 × 1
One can extend this idea to numbers upto lakh as seen in the following
table. (Let us call them placement boxes). Fill the entries in the blanks left.
Number TLakh Lakh TTh Th H T O Number Name Expansion
7,34,543 — 7 3 4 5 4 3 Seven lakh thirty four thousand five -----------------
hundred forty three
32,75,829 3 2 7 5 8 2 9 --------------------- 3 × 10,00,000
+ 2 × 1,00,000
+ 7 × 10,000
+ 5 × 1000
+ 8 × 100
+ 2 × 10 + 9
Similarly, we may include numbers upto crore as shown below :
Number TCr Cr TLakh Lakh TTh Th H T O Number Name
2,57,34,543 — 2 5 7 3 4 5 4 3 ...................................
65,32,75,829 6 5 3 2 7 5 8 2 9 Sixty five crore thirty
two lakh seventy five
thousand eight hundred
twenty nine
You can make other formats of tables for writing the numbers in expanded form.
MATHEMATICS
10
Use of commas
You must have noticed that in writing large numbers in the
sections above, we have often used commas. Commas help us
in reading and writing large numbers. In our Indian System
of Numeration we use ones, tens, hundreds, thousands and
then lakhs and crores. Commas are used to mark thousands,
lakhs and crores. The first comma comes after hundreds place (three digits from the
right) and marks thousands. The second comma comes two digits later (five digits
from the right). It comes after ten thousands place and marks lakh. The third comma
comes after anothertwodigits(seven digits from the right). Itcomes after ten lakh
place and marks crore.
For example, 5, 08, 01, 592
3, 32, 40, 781
7, 27, 05, 062
Try reading the numbers given above. Write five more numbers in this form and
read them.
International System of Numeration
In the International System of Numeration, as it is being used we have ones,
tens, hundreds, thousands and then millions. One million is a thousand
thousands. Commas are used to mark thousands and millions. It comes after
every three digits from the right. The first comma marks thousands and the
next comma marks millions. For example, the number 50,801,592 is read in
the International System as fifty million eight hundred one thousand five
hundred ninety two. In the Indian System, it is five crore eight lakh one thousand
five hundred ninety two.
How many lakhs make a million?
How many millions make a crore?
Take three large numbers. Express them in both Indian and International
Numeration systems.
This may interest you :
To express numbers larger than a million, a billion is used in the International
System of Numeration: 1 billion = 1000 million.
While writing
number names,
we do not use
commas.
KNOWING OUR NUMBERS
11
How much was the increase during
1991-2001? Try to find out.
Do you know what is India’s population
today? Try to find this too.
1. Read these numbers. Write them using placement boxes and then write
their expanded forms.
(i) 475320 (ii) 9847215 (iii) 97645310 (iv) 30458094
(a) Which is the smallest number?
(b) Which is the greatest number?
(c) Arrange these numbers in ascending and descending orders.
2. Read these numbers.
(i) 527864 (ii) 95432 (iii) 18950049 (iv) 70002509
(a) Write these numbers using placement boxes and then using commas in
Indian as well as International System of Numeration..
(b) Arrange these in ascending and descending order.
3. Take three more groups of large numbers and do the exercise given above.
Do you know?
India’s population increased by
27 million during 1921-1931;
37 million during 1931-1941;
44 million during 1941-1951;
78 million during 1951-1961!
1.3 Large Numbers in Practice
In earlier classes, we have learnt that we use centimetre (cm) as a unit of length.
For measuring the length of a pencil, the width of a book or
notebooks etc., we use centimetres. Our ruler has marks on each centimetre.
For measuring the thickness of a pencil, however, we find centimetre too big.
We use millimetre (mm) to show the thickness of a pencil.
(a) 10 millimetres = 1 centimetre
To measure the length of the classroom or
the school building, we shall find
centimetre too small. We use metre for the
purpose.
(b) 1 metre = 100 centimetres
= 1000 millimetres
Even metre is too small, when we have to
state distances between cities, say, Delhi
and Mumbai, or Chennai and Kolkata. For
this we need kilometres (km).
(c) 1 kilometre = 1000 metres
How many millimetres make 1 kilometre?
Since 1 m = 1000 mm
1 km = 1000 m = 1000 × 1000 mm = 10,00,000 mm
We go to the market to buy rice or wheat; we buy it in
kilograms (kg). But items like ginger or chillies which
we do not need in large quantities, we buy in grams (g).
We know 1 kilogram = 1000 grams.
Have you noticed the weight of the medicine tablets
given to the sick? It is very small. It is in milligrams
(mg).
1 gram = 1000 milligrams.
What is the capacity of a bucket for holding water? It
is usually 20 litres (
**

Questions

**A.**
a number which is divisible by 1 and itself is called a prime number.
for example, 7,3,5,11 etc
link

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answer

6 years, 5 months ago

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