NCERT Revision notes for class 6 Maths Knowing our numbers

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What are Numbers?

Ans: Numbers are the mathematical symbols that are used to count objects or we can also say that Numbers are the combination of digits. Example: 23, 67, 2098, 33, 9, 7, 5

Smallest __ digit numbers
Largest/greatest __ digit numbers

1. Smallest ___ digit numbers

How to find smallest __ digit numbers?

Ans: Smallest __ digit numbers' rule: To find the smallest __ digit number we must use the combination of 1 and 0.

Example Questions related to smallest digit numbers.

Q1. Smallest 1 digit number?

Ans: 0

Q2. Smallest 5 digit number?

Ans: 10,000

Q3. Smallest 3 digit number?

Ans: 100

Q4. Smallest 8 digit number?

Ans: 1,00,00,000

2. Largest __ digit number

Ans: Largest __ digit numbers' rule: To find the Largest __ digit number we must use the combination of only 9.

Example Questions related to largest digit numbers.

Q1. Largest 1 digit number?

Ans: 9

Q2. Largest 4 digit number?

Ans: 9,999

Q3. Largest 8 digit number?

Ans: 9,99,99,999

Indian system of numeration
Places

Indian system of numeration

In Indian system of numeration, the places are written as follows:

Places:

Places according to Indian System of numeration
Short form	Long form
O	Ones
T	Tens
H	Hundred
Th.	Thousand
T.Th	Ten Thousand
L	Lakh
T.L	Ten Lakh
C	Crore
T.C	Ten Crore

Rules for writing spellings:

Write the spelling of digit(s)
Write the spelling of its/their place

Example questions:
Q1. Write number name of 2,34,23,523 according to Indian system of numeration.

Solve: Finding places of the digits from right side:

3 - Ones
2 - Tens
5 - Hundred
3 - Thousand
2 - Ten thousand
4 - Lakh
3 - Ten Lakh
2 - Crore

Spelling: Two crore thirty four lakh twenty three thousand five hundred twenty three.

Q2. Write number name of 57,98,264 according to Indian System of numeration.

Solve: Finding places of the digits from right side:

4 - ones
6 - tens
2 - hundred
8 - thousand
9 - ten thousand
7 - lakh
5 - ten lakh

Spelling: fifty seven lakh ninty eight thousand two hundred sixty four.

Q3. Write the number name of 10,50,507 according to Indian system of numeration.

Solve: Finding places of the digits from right side:

7 - ones
0 - tens
5 - hundred
0 - thousand
5 - ten thousand
0 - lakh
1 - ten lakh

Spelling: Ten lakh fifty thousand five hundred seven.

International system of numeration

In International system of numeration, the places are written as follows:

Places as per International system of numeration
Short form	Long form
O	ones
T	tens
H	Hundred
Th	thousand
T.Th	Ten thousand
H.th	Hundred thousand
M	million
T.M	Ten milllion

Rules for writing spellings:

Write the spelling of digit(s)
Write the spelling of its/their place

Example questions:

Q1. write the spelling of 23,523,532 as per International system of numeration.

Ans:

Step 1: finding places of each digit from right to left

2 - ones

3 - tens

5 - hundred

3 - thousand

2 - ten thousand

5 - hundred thousand

3 - million

2 - ten million

Step 2 (writing spelling): Twenty three million five hundred twenty three thousand five hundred thirty two.

Q2. Write the spelling of 7,462,574 as per international system of numeration.

Ans:

Step 1: Finding places of each digit from right to left:

4 - ones

7 - tens

5 - hundred

2 - thousand

6 - ten thousand

4 - hundred thousand

7 - million

Step 2 (writing spelling): seven million four hundred sixty two thousand five hundred seventy four.

Estimation or rounding off

Round off nearest 10

Rules:

If unit digit < 5

replace the unit digit with 0 and write all

the digits as it is.

If unit digit is = 5

replace the unit digit with 0 and add 1 to

its immediate next digit and write it down

as well.

If unit digit > 5

replace the unit digit with 0 and add 1 to

its immediate next digit and write it down

as well

Let's look at an example:

To round off any number to nearest 10 (take for example 56) . Folllow the below steps:

Find the half of 10 which is 5.
Since 5 is a single digit, its place will always be ones
Now, compare the unit digit of 56 with 5. Here the unit digit of 56 is 6, which is bigger than 5.
So, we have to replace 6 with 0 and we must also add 1 to 5, which makes 56 as 60 after rounding off to nearest 10.

Round off nearest 100

Rules:

If last two digit < 50

replace the last two digits with 0 and write all

the digits as it is.

If last two digit = 50

replace the last two digits with 0 and add 1 to

its immediate next digit and write it down

as well.

If last two digit > 50

replace the last two digits with 0 and add 1 to

its immediate next digit and write it down

as well

Let's look at an example:

To round off any number to nearest 100 (take for example 566) . Folllow the below steps:

Find the half of 100 which is 50.
Since 50 has two digits.
Now, compare the last two digits of 566 with 50. Here the last two digits (66) are bigger than 50.
So, we have to replace 66 with 00 and we must also add 1 to 5, which makes 566 as 600 after rounding off to nearest 100.

Round off nearest 1000

Rules:

If last three digit < 500

replace the last three digits with three 0s and write all

the digits as it is.

If last three digit = 500

replace the last three digits with three 0s and add 1 to

its immediate next digit and write it down

as well.

If last three digit > 500

replace the last three digits with three 0s and add 1 to

its immediate next digit and write it down

as well

Let's look at an example:

To round off any number to nearest 1000 (take for example 5476) . Folllow the below steps:

Find the half of 1000 which is 500.
Since 500 has three digits.
Now, compare the last three digits of 5476 with 500. Here the last three digits (476) are smaller than 500.
So, we have to replace 476 with 000 and we must write the 5 as it is, which makes 5476 as 5000 after rounding off to nearest 1000.

Roman numbers

The table for roman numbers is given below:

Roman numbers	Hindu-Arabic numeral
I	1
II	2
III	3
IV	4
V	5
VI	6
VII	7
VIII	8
IX	9
X	10
XX	20
XXX	30
XL	40
L	50
LX	60
LXX	70
LXXX	80
XC	90
C	100
CD	400
D	500
M	1000

Related NCERT Revision notes

Whole numbers