Arranging Decimals in Ascending/Descending Order - Math Worksheets ... - Free Printable

To solve the problem of ordering the given sets of decimal numbers in ascending or descending order, we need to carefully compare the numbers digit by digit. Here's a step-by-step explanation for each part:

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1. Ascending Order:

Numbers: 56.9, 56.98, 56.278, 5.699

- Step 1: Compare the whole number parts first.
- The smallest whole number is 5 (from 5.699).
- The next smallest whole number is 56 (from 56.9, 56.98, and 56.278).

- Step 2: For numbers with the same whole number part (56), compare the decimal parts.
- 56.278 < 56.9 < 56.98.

- Final Order:
5.699, 56.278, 56.9, 56.98

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2. Descending Order:

Numbers: 137.687, 136.2, 137.788, 136.567

- Step 1: Compare the whole number parts first.
- The largest whole number is 137 (from 137.687 and 137.788).
- The next largest whole number is 136 (from 136.2 and 136.567).

- Step 2: For numbers with the same whole number part (137), compare the decimal parts.
- 137.788 > 137.687.
- For numbers with the same whole number part (136), compare the decimal parts.
- 136.567 > 136.2.

- Final Order:
137.788, 137.687, 136.567, 136.2

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3. Descending Order:

Numbers: 6.900, 6.909, 6.009, 6.09

- Step 1: Compare the whole number parts first.
- All numbers have the same whole number part, which is 6.

- Step 2: Compare the decimal parts.
- 6.909 > 6.900 > 6.09 > 6.009.

- Final Order:
6.909, 6.900, 6.09, 6.009

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4. Ascending Order:

Numbers: 400.60, 40.444, 40.045, 4.699

- Step 1: Compare the whole number parts first.
- The smallest whole number is 4 (from 4.699).
- The next smallest whole number is 40 (from 40.444 and 40.045).
- The largest whole number is 400 (from 400.60).

- Step 2: For numbers with the same whole number part (40), compare the decimal parts.
- 40.045 < 40.444.

- Final Order:
4.699, 40.045, 40.444, 400.60

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5. Ascending Order:

Numbers: 18.298, 18.453, 18.45, 18.682

- Step 1: Compare the whole number parts first.
- All numbers have the same whole number part, which is 18.

- Step 2: Compare the decimal parts.
- 18.298 < 18.45 < 18.453 < 18.682.

- Final Order:
18.298, 18.45, 18.453, 18.682

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6. Descending Order:

Numbers: 10.788, 100.007, 100.072, 100.1

- Step 1: Compare the whole number parts first.
- The largest whole number is 100 (from 100.007, 100.072, and 100.1).
- The smallest whole number is 10 (from 10.788).

- Step 2: For numbers with the same whole number part (100), compare the decimal parts.
- 100.1 > 100.072 > 100.007.

- Final Order:
100.1, 100.072, 100.007, 10.788

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7. Descending Order:

Numbers: 123.29, 1.2329, 1232.9, 12.329

- Step 1: Compare the whole number parts first.
- The largest whole number is 1232 (from 1232.9).
- The next largest whole number is 123 (from 123.29).
- The next largest whole number is 12 (from 12.329).
- The smallest whole number is 1 (from 1.2329).

- Final Order:
1232.9, 123.29, 12.329, 1.2329

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Final Answers:

1. Ascending Order: 5.699, 56.278, 56.9, 56.98
2. Descending Order: 137.788, 137.687, 136.567, 136.2
3. Descending Order: 6.909, 6.900, 6.09, 6.009
4. Ascending Order: 4.699, 40.045, 40.444, 400.60
5. Ascending Order: 18.298, 18.45, 18.453, 18.682
6. Descending Order: 100.1, 100.072, 100.007, 10.788
7. Descending Order: 1232.9, 123.29, 12.329, 1.2329

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{Ascending Order: } 5.699, 56.278, 56.9, 56.98 \\
2. \text{Descending Order: } 137.788, 137.687, 136.567, 136.2 \\
3. \text{Descending Order: } 6.909, 6.900, 6.09, 6.009 \\
4. \text{Ascending Order: } 4.699, 40.045, 40.444, 400.60 \\
5. \text{Ascending Order: } 18.298, 18.45, 18.453, 18.682 \\
6. \text{Descending Order: } 100.1, 100.072, 100.007, 10.788 \\
7. \text{Descending Order: } 1232.9, 123.29, 12.329, 1.2329 \\
\end{array}
}
\]