Mathematics worksheet focusing on comparing and ordering numbers, designed for educational practice.

Problem: Comparing and Ordering Numbers

The task involves comparing numbers, selecting the greatest and smallest numbers in sets, and arranging numbers in descending and ascending orders. Let's solve each part step by step.

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#### 1. Compare the following using >, =, <

We need to compare the given pairs of numbers and determine whether the first number is greater than (>), equal to (=), or less than (<) the second number.

(a) 65772 ____ 65707

- Both numbers have the same digits up to the thousands place (657).
- In the tens place, 65772 has a 7, while 65707 has a 0.
- Since 7 > 0, 65772 > 65707.

(b) 724582 ____ 88899

- The first number (724582) has six digits, while the second number (88899) has five digits.
- Any number with more digits is greater than a number with fewer digits.
- Therefore, 724582 > 88899.

(c) 846470 ____ 847740

- Both numbers have the same digits up to the ten-thousands place (84).
- In the thousands place, 846470 has a 6, while 847740 has a 7.
- Since 6 < 7, 846470 < 847740.

Final Answers for Part 1:
(a) \( 65772 > 65707 \)
(b) \( 724582 > 88899 \)
(c) \( 846470 < 847740 \)

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#### 2. Select the greatest number in each set of numbers

We need to identify the largest number in each given set.

(a) 76050, 75650, 75006, 70605

- Compare the numbers digit by digit:
- All numbers start with 7, so we move to the next digit.
- In the thousands place: 76050 > 75650 > 75006 > 70605.
- The greatest number is 76050.

(b) 118777, 118070, 118007, 118700

- Compare the numbers digit by digit:
- All numbers start with 118, so we move to the next digit.
- In the hundreds place: 118777 > 118700 > 118070 > 118007.
- The greatest number is 118777.

(c) 10040, 10400, 10004, 14000

- Compare the numbers digit by digit:
- All numbers start with 1, so we move to the next digit.
- In the thousands place: 14000 > 10400 > 10040 > 10004.
- The greatest number is 14000.

Final Answers for Part 2:
(a) 76050
(b) 118777
(c) 14000

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#### 3. Select the smallest number in each set

We need to identify the smallest number in each given set.

(a) 28118, 28108, 28008, 28180

- Compare the numbers digit by digit:
- All numbers start with 28, so we move to the next digit.
- In the hundreds place: 28008 < 28108 < 28118 < 28180.
- The smallest number is 28008.

(b) 127582, 125872, 127528, 127258

- Compare the numbers digit by digit:
- All numbers start with 12, so we move to the next digit.
- In the thousands place: 125872 < 127258 < 127528 < 127582.
- The smallest number is 125872.

Final Answers for Part 3:
(a) 28008
(b) 125872

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#### 4. Write the following numbers in descending order

We need to arrange the given numbers from largest to smallest.

Numbers: 1,238; 1,234,456; 17,836; 135,786; 1,143,675

- Compare the numbers by their number of digits:
- 1,143,675 (7 digits)
- 1,234,456 (7 digits)
- 135,786 (6 digits)
- 17,836 (5 digits)
- 1,238 (4 digits)

- Arrange in descending order:
1. 1,143,675
2. 1,234,456
3. 135,786
4. 17,836
5. 1,238

Final Answer for Part 4 (Descending Order):
\[
\boxed{1,143,675, 1,234,456, 135,786, 17,836, 1,238}
\]

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#### Write the following in ascending order

Numbers: 12983476; 10203040; 9747543; 24302065; 18765200

- Compare the numbers by their number of digits:
- All numbers have 8 digits, so we compare them digit by digit.

- Arrange in ascending order:
1. 9747543
2. 10203040
3. 12983476
4. 18765200
5. 24302065

Final Answer for Ascending Order:
\[
\boxed{9747543, 10203040, 12983476, 18765200, 24302065}
\]

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Final Summary of Answers:

1. (a) \( 65772 > 65707 \)
(b) \( 724582 > 88899 \)
(c) \( 846470 < 847740 \)

2. (a) 76050
(b) 118777
(c) 14000

3. (a) 28008
(b) 125872

4. Descending Order: \(\boxed{1,143,675, 1,234,456, 135,786, 17,836, 1,238}\)

Ascending Order: \(\boxed{9747543, 10203040, 12983476, 18765200, 24302065}\)