Math worksheet for ordering numbers from smallest to largest and largest to smallest.

Problem Analysis:

The task involves ordering a set of numbers in ascending order (from smallest to largest) and then writing them in descending order (from largest to smallest). The numbers provided are both whole numbers and decimal numbers. To solve this, we need to carefully compare the numbers and arrange them accordingly.

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Step-by-Step Solution:

#### Part 1: Write these numbers in order, from smallest to largest.

The given numbers are:
\[ 6.675, \quad 3.832, \quad 8.930, \quad 2.612 \]

Step 1: Compare the numbers.
- Start by comparing the whole number parts:
- \( 2.612 \) has the smallest whole number part (2).
- Next is \( 3.832 \) with a whole number part of 3.
- Then \( 6.675 \) with a whole number part of 6.
- Finally, \( 8.930 \) with a whole number part of 8.

Step 2: Arrange in ascending order.
- Since the whole number parts are distinct, the order is straightforward:
\[ 2.612, \quad 3.832, \quad 6.675, \quad 8.930 \]

Answer for Part 1:
\[ \boxed{2.612, 3.832, 6.675, 8.930} \]

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#### Part 2: Write these numbers in order, from largest to smallest.

The given numbers are:
\[ 3.574, \quad 2.631, \quad 8.909, \quad 5.962, \quad 6.853, \quad 3.265 \]

Step 1: Compare the numbers.
- Start by comparing the whole number parts:
- \( 8.909 \) has the largest whole number part (8).
- Next is \( 6.853 \) with a whole number part of 6.
- Then \( 5.962 \) with a whole number part of 5.
- \( 3.574 \) and \( 3.265 \) both have a whole number part of 3, so compare the decimal parts:
- \( 3.574 > 3.265 \).
- Finally, \( 2.631 \) has the smallest whole number part (2).

Step 2: Arrange in descending order.
- Based on the comparisons:
\[ 8.909, \quad 6.853, \quad 5.962, \quad 3.574, \quad 3.265, \quad 2.631 \]

Answer for Part 2:
\[ \boxed{8.909, 6.853, 5.962, 3.574, 3.265, 2.631} \]

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#### Part 3: Write these numbers in order, from smallest to largest.

The given numbers are:
\[ 5.269, \quad 6.920, \quad 4.827, \quad 6.267, \quad 3.720, \quad 9.623, \quad 9.206, \quad 6.215 \]

Step 1: Compare the numbers.
- Start by comparing the whole number parts:
- \( 3.720 \) has the smallest whole number part (3).
- Next is \( 4.827 \) with a whole number part of 4.
- Then \( 5.269 \) with a whole number part of 5.
- \( 6.215 \), \( 6.267 \), and \( 6.920 \) all have a whole number part of 6, so compare the decimal parts:
- \( 6.215 < 6.267 < 6.920 \).
- Finally, \( 9.206 \) and \( 9.623 \) both have a whole number part of 9, so compare the decimal parts:
- \( 9.206 < 9.623 \).

Step 2: Arrange in ascending order.
- Based on the comparisons:
\[ 3.720, \quad 4.827, \quad 5.269, \quad 6.215, \quad 6.267, \quad 6.920, \quad 9.206, \quad 9.623 \]

Answer for Part 3:
\[ \boxed{3.720, 4.827, 5.269, 6.215, 6.267, 6.920, 9.206, 9.623} \]

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#### Part 4: Write these numbers in order, from largest to smallest.

The given numbers are:
\[ 2.802, \quad 6.932, \quad 6.912, \quad 6.926, \quad 6.920, \quad 9.235 \]

Step 1: Compare the numbers.
- Start by comparing the whole number parts:
- \( 9.235 \) has the largest whole number part (9).
- All other numbers have a whole number part of 6 or 2, so compare the decimal parts:
- Among \( 6.932, 6.926, 6.920, 6.912 \):
- \( 6.932 > 6.926 > 6.920 > 6.912 \).
- \( 2.802 \) has the smallest whole number part (2).

Step 2: Arrange in descending order.
- Based on the comparisons:
\[ 9.235, \quad 6.932, \quad 6.926, \quad 6.920, \quad 6.912, \quad 2.802 \]

Answer for Part 4:
\[ \boxed{9.235, 6.932, 6.926, 6.920, 6.912, 2.802} \]

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Final Answers:

1. \( \boxed{2.612, 3.832, 6.675, 8.930} \)
2. \( \boxed{8.909, 6.853, 5.962, 3.574, 3.265, 2.631} \)
3. \( \boxed{3.720, 4.827, 5.269, 6.215, 6.267, 6.920, 9.206, 9.623} \)
4. \( \boxed{9.235, 6.932, 6.926, 6.920, 6.912, 2.802} \)