1. Compare 4978 and 5643…….
5643 is greater as the digit at the thousands place in 5643 is greater than that in 4978.
2. Compare 9364, 8695, 8402 and 7924
9364 is the greatest as it has the greatest digit at the thousands place in all the numbers.
Whereas 7924 is the smallest as it has the smallest digit at the thousands place in all the numbers.
3. Compare 56321 and 56843
Here, we will start by checking the thousands place.As the digit 5 at ten thousand place is same so we will move forward and see the thousands place. The digit 6 is also same so we will still move on further to check the hundreds place.
The digit at the hundreds place in 56843 is greater than that in 56321
Thus 56843 is greater than 56321
Example: Arrange the following heights in ascending and descending order.
Sol:
Ascending order – 90 < 160 < 170 < 185 < 230
Descending order – 230 >185 >170 > 160 > 90
Let us understand the number formation with the help oof an example.
Example:
Form the largest and the smallest possible numbers using 3,8,1,5 without repetition
Largest number will be formed by arranging the given numbers in descending order – 8531
The smallest number will be formed by arranging the given numbers in ascending order – 1358
99 is the greatest 2digit number
999 is the greatest 3digit number
9999 is the greatest 4digit number
Observation
Moving forward, all the above situations are same as adding 1 to the greatest 4digit number is the same as the smallest 5digit number. (9999 + 1 = 10,000), and it is known as ten thousand.
As above pattern if we add 1 to the greatest 5digit number then we will get the smallest 6digit number
(99,999 + 1 = 1,00,000)
This number is called one lakh.
It refers to the positional notation which defines a digits position.
For Example: 6931 Here, 1 is at one's place, 3 is at tens place, 9 is at hundreds place and 6 is at thousands place
It refers to expand the number to see the value of each digit.
For Example:
6821 = 6000 + 800 + 20 + 1
= 6 × 1000 + 8 × 100 + 2 × 10 + 1×1
Introducing 1,00,000
Observations:
1. Addition Pattern:
2. Expanded Form of 6digit Numbers:
To get the larger numbers also, we will follow the same pattern. We will get the smallest 7digit number if we add one more to the greatest 6digit number, which is called Ten Lakh. Going forward if we add 1 to the greatest 7digit number then we will get the smallest 8digit number which is called One Crore.
Remark:
1 hundred = 10 tens
1 thousand = 10 hundreds = 100 tens
1 lakh = 100 thousands = 1000 hundreds
1 crore = 100 lakhs = 10,000 thousands
Pattern
9 + 1 = 10
99 + 1 = 100
999 + 1 = 1000
9,999 + 1 = 10,000
99,999 + 1 =1,00,000
9,99,999 + 1 = 10,00,000
99,99,999 + 1 = 1,00,00,000
We can identify the digits in ones place, tens place and hundreds place in a number by writing them under the tables O, T and H.
AS:
We use commas in large numbers to ease reading and writing. In our Indian System of Numeration, we use ones, tens, hundreds, thousands and then lakhs and crores.
We use the first comma after hundreds place which is three digits from the right. The second comma comes after two digits i.e. five digits from the right. The third comma comes after another two digits which is seven digits from the right.
For Example: 5, 44, 12, 940
Example: Expand 341,697,832
Sol:
Expanded form: 3 x 100,000,000 + 4 x 10,000,000 + 1 x 1,000,000 + 6 x 100,000 + 9 x 10,000 + 7 x 1,000 + 8 x 100 + 3 x 10 + 2 x 1
Remark: If we have to express the numbers larger than a million then we use a billion in the International System of Numeration:
1 billion = 1000 million
Large Numbers in Practice
10 millimeters = 1 centimeter
1 meter = 100 centimeters = 1000 millimeters
1 kilometer = 1000 meters
1 kilogram = 1000 grams.
1 gram = 1000 milligrams.
1 litre = 1000 millilitres
1 litre = 1000 millilitres
Earlier we have learned about the units of length: centimeter (cm) for small measurements like pencils, and meter (m) for larger measurements like classrooms or school buildings. Here are some conversion factors:
(a) 10 millimeters (mm) = 1 centimeter (cm)
(b) 1 meter (m) = 100 centimeters (cm) = 1000 millimeters (mm)
(c) 1 kilometer (km) = 1000 meters (m)
1 km = 1000 m = 1000 × 1000 mm = 10,00,000 mm
Common units share prefixes such as kilo, milli, and centi. Note that kilo is the largest, milli is the smallest, and centi is 100 times smaller.
94 videos347 docs54 tests

1. What are some strategies for comparing numbers effectively? 
2. How can I determine the proper order of numbers? 
3. What does "shifting digits" mean in the context of numbers? 
4. How does the introduction of 10,000 impact number understanding? 
5. Why is it important to use commas in large numbers? 

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