Math worksheet for practicing comparison and ordering of whole numbers.

Problem Analysis:

The task involves comparing and ordering whole numbers. The problems are divided into two main sections:
1. Comparison of Numbers: Using the symbols `<`, `>`, or `=` to compare pairs of numbers.
2. Ordering Numbers: Arranging numbers in ascending (least to greatest) or descending (greatest to least) order.

Let's solve each part step by step.

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Part 1: Comparison of Numbers

#### Instructions:
Compare the given pairs of numbers using `<`, `>`, or `=`.

#### Solutions:

1. 28,940 vs. 28,904
- Compare digit by digit from left to right.
- Both numbers have the same digits in the ten-thousands and thousands places (`28`).
- In the hundreds place, `9` is greater than `0`.
- Therefore, 28,940 > 28,904.

2. 79,112 vs. 79,211
- Compare digit by digit from left to right.
- Both numbers have the same digits in the ten-thousands and thousands places (`79`).
- In the hundreds place, `1` is less than `2`.
- Therefore, 79,112 < 79,211.

3. 54,891 vs. 54,891
- All digits are identical.
- Therefore, 54,891 = 54,891.

4. 80,030 vs. 80,032
- Compare digit by digit from left to right.
- Both numbers have the same digits in the ten-thousands, thousands, and hundreds places (`80,0`).
- In the tens place, `3` is equal for both.
- In the ones place, `0` is less than `2`.
- Therefore, 80,030 < 80,032.

5. 256,025 vs. 256,025
- All digits are identical.
- Therefore, 256,025 = 256,025.

6. 621,438 vs. 999,999
- Compare the number of digits first.
- `621,438` has six digits, while `999,999` also has six digits.
- Compare digit by digit from left to right.
- In the hundred-thousands place, `6` is less than `9`.
- Therefore, 621,438 < 999,999.

7. 809,100 vs. 809,010
- Compare digit by digit from left to right.
- Both numbers have the same digits in the hundred-thousands, ten-thousands, and thousands places (`809`).
- In the hundreds place, `1` is greater than `0`.
- Therefore, 809,100 > 809,010.

8. 29,867 vs. 100,000
- Compare the number of digits first.
- `29,867` has five digits, while `100,000` has six digits.
- A number with fewer digits is always smaller.
- Therefore, 29,867 < 100,000.

9. 999,009 vs. 999,998
- Compare digit by digit from left to right.
- Both numbers have the same digits in the hundred-thousands, ten-thousands, and thousands places (`999`).
- In the hundreds place, `0` is less than `9`.
- Therefore, 999,009 < 999,998.

10. 535,427 vs. 535,428
- Compare digit by digit from left to right.
- Both numbers have the same digits in the hundred-thousands, ten-thousands, thousands, hundreds, and tens places (`535,42`).
- In the ones place, `7` is less than `8`.
- Therefore, 535,427 < 535,428.

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Part 2: Ordering Numbers

#### Instructions:
Arrange the given sets of numbers in ascending (least to greatest) or descending (greatest to least) order.

#### Solutions:

11. Order from least to greatest: 32,201; 32,120; 32,102
- Compare the numbers digit by digit.
- All numbers have the same digits in the ten-thousands and thousands places (`32`).
- In the hundreds place, `1` is less than `2`.
- In the tens place, `0` is less than `2`.
- In the ones place, `2` is less than `1`.
- Ordered: 32,102 < 32,120 < 32,201.

12. Order from greatest to least: 441,025; 441,025; 439,250
- Compare the numbers digit by digit.
- All numbers have the same digits in the hundred-thousands and ten-thousands places (`441`).
- In the hundreds place, `0` is less than `3`.
- Ordered: 441,025 = 441,025 > 439,250.

13. Order from greatest to least: 62,875; 62,578; 62,785
- Compare the numbers digit by digit.
- All numbers have the same digits in the ten-thousands and thousands places (`62`).
- In the hundreds place, `8` is greater than `7` and `5`.
- In the tens place, `7` is greater than `5`.
- Ordered: 62,875 > 62,785 > 62,578.

14. Order from least to greatest: 331,754; 332,457; 331,547
- Compare the numbers digit by digit.
- All numbers have the same digits in the hundred-thousands and ten-thousands places (`331`).
- In the hundreds place, `5` is less than `7` and `4`.
- In the tens place, `4` is less than `5`.
- Ordered: 331,547 < 331,754 < 332,457.

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Part 3: Identifying the Larger Number

#### Instructions:
Determine which number is larger among the given options.

#### Solution:

15. Which number is larger than 345,827?
- Compare each option with `345,827`:
- a. 345,382: All digits are the same up to the hundreds place. In the tens place, `8` is greater than `3`. So, `345,827 > 345,382`.
- b. 354,538: The hundreds place is `5`, which is greater than `4` in `345,827`. So, `354,538 > 345,827`.
- c. 345,238: All digits are the same up to the hundreds place. In the tens place, `8` is greater than `2`. So, `345,827 > 345,238`.
- d. 345,328: All digits are the same up to the hundreds place. In the tens place, `8` is greater than `3`. So, `345,827 > 345,328`.

- The only number larger than `345,827` is 354,538.

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Final Answers:

1. 28,940 > 28,904
2. 79,112 < 79,211
3. 54,891 = 54,891
4. 80,030 < 80,032
5. 256,025 = 256,025
6. 621,438 < 999,999
7. 809,100 > 809,010
8. 29,867 < 100,000
9. 999,009 < 999,998
10. 535,427 < 535,428
11. 32,102 < 32,120 < 32,201
12. 441,025 = 441,025 > 439,250
13. 62,875 > 62,785 > 62,578
14. 331,547 < 331,754 < 332,457
15. b. 354,538

Boxed Final Answer:
\[
\boxed{b}
\]