Comparing and Ordering Decimals (Worksheets) - Free Printable

Problem: Ordering Numbers: Decimals

The task is to rewrite each list of numbers in order, from least to greatest. Let's solve each part step by step.

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#### Part a:
Numbers: \( 4.5, 4.05, 5.4, 5.45, 5 \)

1. Compare the whole number parts first:
- The smallest whole number is 4 (in \( 4.5 \) and \( 4.05 \)).
- The next smallest whole number is 5 (in \( 5.4 \), \( 5.45 \), and \( 5 \)).

2. Compare the decimal parts for numbers with the same whole number:
- For numbers starting with 4:
- \( 4.05 \) (decimal part is 0.05)
- \( 4.5 \) (decimal part is 0.5)
- Since \( 0.05 < 0.5 \), \( 4.05 < 4.5 \).
- For numbers starting with 5:
- \( 5 \) (no decimal part, so it is smaller than any number with a decimal part starting with 5).
- \( 5.4 \) (decimal part is 0.4)
- \( 5.45 \) (decimal part is 0.45)
- Since \( 0.4 < 0.45 \), \( 5.4 < 5.45 \).

3. Final order:
- \( 4.05, 4.5, 5, 5.4, 5.45 \)

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#### Part b:
Numbers: \( 3.2, 3, 2.03, 2.02, 2.23 \)

1. Compare the whole number parts first:
- The smallest whole number is 2 (in \( 2.03 \), \( 2.02 \), and \( 2.23 \)).
- The next smallest whole number is 3 (in \( 3.2 \) and \( 3 \)).

2. Compare the decimal parts for numbers with the same whole number:
- For numbers starting with 2:
- \( 2.02 \) (decimal part is 0.02)
- \( 2.03 \) (decimal part is 0.03)
- \( 2.23 \) (decimal part is 0.23)
- Since \( 0.02 < 0.03 < 0.23 \), \( 2.02 < 2.03 < 2.23 \).
- For numbers starting with 3:
- \( 3 \) (no decimal part, so it is smaller than \( 3.2 \)).

3. Final order:
- \( 2.02, 2.03, 2.23, 3, 3.2 \)

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#### Part c:
Numbers: \( 0.1, 0, 1.01, 1, 0.01 \)

1. Compare the whole number parts first:
- The smallest whole number is 0 (in \( 0 \) and \( 0.01 \)).
- The next smallest whole number is 1 (in \( 1.01 \) and \( 1 \)).

2. Compare the decimal parts for numbers with the same whole number:
- For numbers starting with 0:
- \( 0 \) (no decimal part)
- \( 0.01 \) (decimal part is 0.01)
- \( 0.1 \) (decimal part is 0.1)
- Since \( 0 < 0.01 < 0.1 \), \( 0 < 0.01 < 0.1 \).
- For numbers starting with 1:
- \( 1 \) (no decimal part)
- \( 1.01 \) (decimal part is 0.01)
- Since \( 0 < 0.01 \), \( 1 < 1.01 \).

3. Final order:
- \( 0, 0.01, 0.1, 1, 1.01 \)

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#### Part d:
Numbers: \( 9.08, 8.98, 98.1, 9.8, 9.88 \)

1. Compare the whole number parts first:
- The smallest whole number is 8 (in \( 8.98 \)).
- The next smallest whole number is 9 (in \( 9.08 \), \( 9.8 \), and \( 9.88 \)).
- The largest whole number is 98 (in \( 98.1 \)).

2. Compare the decimal parts for numbers with the same whole number:
- For numbers starting with 9:
- \( 9.08 \) (decimal part is 0.08)
- \( 9.8 \) (decimal part is 0.8)
- \( 9.88 \) (decimal part is 0.88)
- Since \( 0.08 < 0.8 < 0.88 \), \( 9.08 < 9.8 < 9.88 \).

3. Final order:
- \( 8.98, 9.08, 9.8, 9.88, 98.1 \)

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Final Answers:

\[
\boxed{
\begin{array}{l}
\text{a. } 4.05, 4.5, 5, 5.4, 5.45 \\
\text{b. } 2.02, 2.03, 2.23, 3, 3.2 \\
\text{c. } 0, 0.01, 0.1, 1, 1.01 \\
\text{d. } 8.98, 9.08, 9.8, 9.88, 98.1 \\
\end{array}
}
\]