Number System — Exercise 1(B)

Fill each of the boxes with the correct symbol > or < :

98,760 $\boxed{\phantom{12345}}$ 1,02,345

Answer

On comparing 98,760 and 1,02,345,

The number 98,760 has 5 digits.

The number 1,02,345 has 6 digits.

When comparing two positive whole numbers, the number with more digits is always the larger number.

Hence, 98,760 < 1,02,345.

5,43,210 $\boxed{\phantom{12345}}$ 98,306

Answer

On comparing 5,43,210 and 98,306,

The number 5,43,210 has 6 digits.

The number 98,306 has 5 digits.

When comparing two positive whole numbers, the number with more digits is always the larger number.

Hence, 5,43,210 > 98,306.

2,13,576 $\boxed{\phantom{12345}}$ 67,531

Answer

On comparing 2,13,576 and 67,531,

The number 2,13,576 has 6 digits.

The number 67,531 has 5 digits.

When comparing two positive whole numbers, the number with more digits is always the larger number.

Hence, 2,13,576 > 67,531.

3,02,368 $\boxed{\phantom{12345}}$ 50,545

Answer

On comparing 3,02,368 and 50,545,

The number 3,02,368 has 6 digits.

The number 50,545 has 5 digits.

When comparing two positive whole numbers, the number with more digits is always the larger number.

Hence, 3,02,368 > 50,545.

76,134 $\boxed{\phantom{12345}}$ 76,079

Answer

On comparing 76,134 and 76,079,

Both numbers have 5 digits.

When the number of digits is the same, we start comparing from the leftmost digit (the highest place value).

Compare the digits in each place value, moving from left to right:

Tens Thousands Place (Leftmost digit):

In 76,134, the digit is 7.

In 76,079, the digit is 7.

Result: These digits are the same. We need to move to the next place value.

Thousands Place:

In 76,134, the digit is 6.

In 76,079, the digit is 6.

Result: These digits are also the same. Move to the next place value.

Hundreds Place:

In 76,134, the digit is 1.

In 76,079, the digit is 0.

Result: Here, 1 is greater than 0.

Hence, 76,134 > 76,079.

6,40,729 $\boxed{\phantom{12345}}$ 6,41,304

Answer

On comparing 6,40,729 and 6,41,304,

Both numbers have 6 digits.

When the number of digits is the same, we start comparing from the leftmost digit (the highest place value).

Compare the digits in each place value, moving from left to right:

Lakhs Place (Leftmost digit):

In 6,40,729, the digit is 6.

In 6,41,304, the digit is 6.

Result: These digits are the same. We need to move to the next place value.

Tens Thousands Place :

In 6,40,729, the digit is 4.

In 6,41,304, the digit is 4.

Result: These digits are the same. We need to move to the next place value.

Thousands Place:

In 6,40,729, the digit is 0.

In 6,41,304, the digit is 1.

Result: Here, 1 is greater than 0.

Hence, 6,40,729 < 6,41,304.

35,79,018 $\boxed{\phantom{12345}}$ 35,80,024

Answer

On comparing 35,79,018 and 35,80,024,

Both numbers have 7 digits.

When the number of digits is the same, we start comparing from the leftmost digit (the highest place value).

Compare the digits in each place value, moving from left to right:

Ten Lakhs Place (Leftmost digit):

In 35,79,018, the digit is 3.

In 35,80,024, the digit is 3.

Result: These digits are the same. We need to move to the next place value.

Lakhs Place :

In 35,79,018, the digit is 5.

In 35,80,024, the digit is 5.

Result: These digits are the same. We need to move to the next place value.

Tens Thousands Place :

In 35,79,018, the digit is 7.

In 35,80,024, the digit is 8.

Result: Here, 8 is greater than 7.

Hence, 35,79,018 < 35,80,024.

83,21,067 $\boxed{\phantom{12345}}$ 83,12,076

Answer

On comparing 83,21,067 and 83,12,076,

Both numbers have 7 digits.

When the number of digits is the same, we start comparing from the leftmost digit (the highest place value).

Compare the digits in each place value, moving from left to right:

Ten Lakhs Place (Leftmost digit):

In 83,21,067, the digit is 8.

In 83,12,076, the digit is 8.

Result: These digits are the same. We need to move to the next place value.

Lakhs Place :

In 83,21,067, the digit is 3.

In 83,12,076, the digit is 3.

Result: These digits are the same. We need to move to the next place value.

Tens Thousands Place :

In 83,21,067, the digit is 2.

In 83,12,076, the digit is 1.

Result: Here, 2 is greater than 1.

Hence, 83,21,067 > 83,12,076.

54,63,217 $\boxed{\phantom{12345}}$ 54,62,378

Answer

On comparing 54,63,217 and 54,62,378,

Both numbers have 7 digits.

When the number of digits is the same, we start comparing from the leftmost digit (the highest place value).

Compare the digits in each place value, moving from left to right:

Ten Lakhs Place (Leftmost digit):

In 54,63,217, the digit is 5.

In 54,62,378, the digit is 5.

Result: These digits are the same. We need to move to the next place value.

Lakhs Place :

In 54,63,217, the digit is 4.

In 54,62,378, the digit is 4.

Result: These digits are the same. We need to move to the next place value.

Tens Thousands Place :

In 54,63,217, the digit is 6.

In 54,62,378, the digit is 6.

Result: These digits are the same. We need to move to the next place value.

Thousands Place :

In 54,63,217, the digit is 3.

In 54,62,378, the digit is 2.

Result: Here, 3 is greater than 2.

Hence, 54,63,217 > 54,62,378.

35,780,624 $\boxed{\phantom{12345}}$ 35,876,002

Answer

On comparing 35,780,624 and 35,876,002,

Both numbers have 8 digits.

When the number of digits is the same, we start comparing from the leftmost digit (the highest place value).

Compare the digits in each place value, moving from left to right:

Ten Millions Place (Leftmost digit):

In 35,780,624, the digit is 3.

In 35,876,002, the digit is 3.

Result: These digits are the same. We need to move to the next place value.

Millions Place :

In 35,780,624, the digit is 5.

In 35,876,002, the digit is 5.

Result: These digits are the same. We need to move to the next place value.

Hundreds Thousands Place :

In 35,780,624, the digit is 7.

In 35,876,002, the digit is 8.

Result: Here, 8 is greater than 7.

Hence, 35,780,624 < 35,876,002.

Arrange the following numbers in ascending order:

57,860,    60,375,    57,906,    61,435,    60,296, 61,380

Answer

Given, 57,860,    60,375,    57,906,    61,435,    60,296, 61,380

To arrange the numbers in ascending order, we compare them digit by digit, starting from the leftmost digit.

Hence, 57,860 < 57,906 < 60,296 < 60,375 < 61,380 < 61,435.

Arrange the following numbers in ascending order:

7,15,840,    98,756,    8,94,105,    17,18,195,    98,678,    8,95,103

Answer

Given, 7,15,840,    98,756,    8,94,105,    17,18,195,    98,678,    8,95,103

To arrange the numbers in ascending order, we compare them digit by digit, starting from the leftmost digit.

Hence, 98,678 < 98,756 < 7,15,840 < 8,94,105 < 8,95,103 < 17,18,195.

Arrange the following numbers in ascending order:

5,01,462,    5,01,076,    5,00,984,    5,02,000,    5,10,010,    4,56,780

Answer

Given, 5,01,462,    5,01,076,    5,00,984,    5,02,000,    5,10,010,    4,56,780

To arrange the numbers in ascending order, we compare them digit by digit, starting from the leftmost digit.

Hence, 4,56,780 < 5,00,984 < 5,01,076 < 5,01,462 < 5,02,000 < 5,10,010.

Arrange the following numbers in descending order:

16,13,241,    7,54,328,    7,52,987,    16,04,895,    7,53,024,    16,20,342

Answer

Given, 16,13,241,    7,54,328,    7,52,987,    16,04,895,    7,53,024,    16,20,342

To arrange the numbers in descending order, we compare them digit by digit, starting from the leftmost digit.

Hence, 16,20,342 > 16,13,241 > 16,04,895 > 7,54,328 > 7,53,024 > 7,52,987.

Arrange the following numbers in descending order:

93,68,516,    1,05,40,603,    9,10,32,401,    93,67,839,    1,05,41,201

Answer

Given, 93,68,516,    1,05,40,603,    9,10,32,401,    93,67,839,    1,05,41,201

To arrange the numbers in descending order, we compare them digit by digit, starting from the leftmost digit.

Hence, 9,10,32,401 > 1,05,41,201 > 1,05,40,603 > 93,68,516 > 93,67,839.

Arrange the following numbers in descending order:

1,48,65,710,    2,05,07,106,    3,00,08,215,    27,86,789,    28,76,879

Answer

Given, 1,48,65,710,    2,05,07,106,    3,00,08,215,    27,86,789,    28,76,879

To arrange the numbers in descending order, we compare them digit by digit, starting from the leftmost digit.

Hence, 3,00,08,215 > 2,05,07,106 > 1,48,65,710 > 28,76,879 > 27,86,789.