Comparing decimals worksheet with 12 exercises for math practice.

Problem Description:

The task involves comparing decimal numbers and filling in the circles with either `<` (less than) or `>` (greater than) to indicate the relationship between the two numbers in each pair.

Solution Approach:

To solve this problem, we need to compare each pair of decimal numbers step by step. Here's how we can do it:

1. Align the decimal points: Ensure both numbers in a pair have the same number of decimal places by adding trailing zeros if necessary.
2. Compare digit by digit: Starting from the leftmost digit, compare each corresponding digit in the two numbers. The first digit where they differ will determine which number is larger.
3. Determine the relationship: Use `<` if the first number is smaller, and `>` if the first number is larger.

Step-by-Step Solution:

#### 1. \( 5.43 \) vs \( 5.34 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 5 = 5 \)
- Second digit (tenths place): \( 4 > 3 \)
- Conclusion: \( 5.43 > 5.34 \)

#### 2. \( 4.53 \) vs \( 9.31 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 4 < 9 \)
- Conclusion: \( 4.53 < 9.31 \)

#### 3. \( 8.32 \) vs \( 8.33 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 8 = 8 \)
- Second digit (tenths place): \( 3 = 3 \)
- Third digit (hundredths place): \( 2 < 3 \)
- Conclusion: \( 8.32 < 8.33 \)

#### 4. \( 6.65 \) vs \( 9.75 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 6 < 9 \)
- Conclusion: \( 6.65 < 9.75 \)

#### 5. \( 8.74 \) vs \( 8.25 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 8 = 8 \)
- Second digit (tenths place): \( 7 > 2 \)
- Conclusion: \( 8.74 > 8.25 \)

#### 6. \( 8.25 \) vs \( 8.25 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 8 = 8 \)
- Second digit (tenths place): \( 2 = 2 \)
- Third digit (hundredths place): \( 5 = 5 \)
- Conclusion: \( 8.25 = 8.25 \) (though the question asks for `<` or `>`, we note equality here)

#### 7. \( 0.65 \) vs \( 0.86 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 0 = 0 \)
- Second digit (tenths place): \( 6 < 8 \)
- Conclusion: \( 0.65 < 0.86 \)

#### 8. \( 0.56 \) vs \( 5.36 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 0 < 5 \)
- Conclusion: \( 0.56 < 5.36 \)

#### 9. \( 5.26 \) vs \( 5.19 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 5 = 5 \)
- Second digit (tenths place): \( 2 > 1 \)
- Conclusion: \( 5.26 > 5.19 \)

#### 10. \( 1.03 \) vs \( 1.12 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 1 = 1 \)
- Second digit (tenths place): \( 0 < 1 \)
- Conclusion: \( 1.03 < 1.12 \)

#### 11. \( 1.21 \) vs \( 8.98 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 1 < 8 \)
- Conclusion: \( 1.21 < 8.98 \)

#### 12. \( 8.88 \) vs \( 8.89 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 8 = 8 \)
- Second digit (tenths place): \( 8 = 8 \)
- Third digit (hundredths place): \( 8 < 9 \)
- Conclusion: \( 8.88 < 8.89 \)

#### 13. \( 9.36 \) vs \( 3.65 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 9 > 3 \)
- Conclusion: \( 9.36 > 3.65 \)

#### 14. \( 3.96 \) vs \( 7.04 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 3 < 7 \)
- Conclusion: \( 3.96 < 7.04 \)

#### 15. \( 7.44 \) vs \( 7.24 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 7 = 7 \)
- Second digit (tenths place): \( 4 > 2 \)
- Conclusion: \( 7.44 > 7.24 \)

#### 16. \( 3.32 \) vs \( 3.23 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 3 = 3 \)
- Second digit (tenths place): \( 3 > 2 \)
- Conclusion: \( 3.32 > 3.23 \)

#### 17. \( 2.33 \) vs \( 5.57 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 2 < 5 \)
- Conclusion: \( 2.33 < 5.57 \)

#### 18. \( 5.75 \) vs \( 7.55 \)
- Align: Both numbers already have the same number of decimal places.
- Compare:
- First digit (integer part): \( 5 < 7 \)
- Conclusion: \( 5.75 < 7.55 \)

Final Answers:

\[
\begin{aligned}
1. & \quad 5.43 > 5.34 \\
2. & \quad 4.53 < 9.31 \\
3. & \quad 8.32 < 8.33 \\
4. & \quad 6.65 < 9.75 \\
5. & \quad 8.74 > 8.25 \\
6. & \quad 8.25 = 8.25 \\
7. & \quad 0.65 < 0.86 \\
8. & \quad 0.56 < 5.36 \\
9. & \quad 5.26 > 5.19 \\
10. & \quad 1.03 < 1.12 \\
11. & \quad 1.21 < 8.98 \\
12. & \quad 8.88 < 8.89 \\
13. & \quad 9.36 > 3.65 \\
14. & \quad 3.96 < 7.04 \\
15. & \quad 7.44 > 7.24 \\
16. & \quad 3.32 > 3.23 \\
17. & \quad 2.33 < 5.57 \\
18. & \quad 5.75 < 7.55 \\
\end{aligned}
\]

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
1. & \quad > \\
2. & \quad < \\
3. & \quad < \\
4. & \quad < \\
5. & \quad > \\
6. & \quad = \\
7. & \quad < \\
8. & \quad < \\
9. & \quad > \\
10. & \quad < \\
11. & \quad < \\
12. & \quad < \\
13. & \quad > \\
14. & \quad < \\
15. & \quad > \\
16. & \quad > \\
17. & \quad < \\
18. & \quad < \\
\end{aligned}
}
\]