Decimals on a Number Line Worksheets - Math Monks - Free Printable

Problem: Comparing Decimals on a Number Line

The task involves completing number lines and comparing given decimal numbers using the symbols \( > \) or \( < \). Let's solve each part step by step.

---

#### 1.
Number line:
```
<---|---|---|---|---|---|---|--->
0.8 1.1 2 2.3 2.9
```
- The missing values can be determined by observing the intervals between the given points.
- The interval between consecutive marks appears to be 0.3.
- Filling in the blanks:
- Between 0.8 and 1.1: \( 0.8 + 0.3 = 1.1 \) (already given).
- Next mark after 1.1: \( 1.1 + 0.3 = 1.4 \).
- Next mark after 1.4: \( 1.4 + 0.3 = 1.7 \).
- Next mark after 1.7: \( 1.7 + 0.3 = 2.0 \) (already given).
- Next mark after 2.0: \( 2.0 + 0.3 = 2.3 \) (already given).
- Next mark after 2.3: \( 2.3 + 0.3 = 2.6 \).

Completed number line:
```
<---|---|---|---|---|---|---|--->
0.8 1.1 1.4 1.7 2.0 2.3 2.6 2.9
```

Comparison: \( 0.8 \, ? \, 2.9 \)
- Since 0.8 is to the left of 2.9 on the number line, \( 0.8 < 2.9 \).

Answer for 1:
\[
\boxed{<}
\]

---

#### 2.
Number line:
```
<---|---|---|---|---|---|--->
4.6 6.6 7.1
```
- The interval between 4.6 and 6.6 is \( 6.6 - 4.6 = 2.0 \).
- The interval between 6.6 and 7.1 is \( 7.1 - 6.6 = 0.5 \).
- Filling in the blanks:
- Next mark after 4.6: \( 4.6 + 1.0 = 5.6 \).
- Next mark after 5.6: \( 5.6 + 1.0 = 6.6 \) (already given).
- Next mark after 6.6: \( 6.6 + 0.5 = 7.1 \) (already given).

Completed number line:
```
<---|---|---|---|---|---|--->
4.6 5.6 6.6 7.1
```

Comparison: \( 6.6 \, ? \, 4.6 \)
- Since 6.6 is to the right of 4.6 on the number line, \( 6.6 > 4.6 \).

Answer for 2:
\[
\boxed{>}
\]

---

#### 3.
Number line:
```
<---|---|---|---|---|---|--->
8.3 10.4 11.1 13.2
```
- The interval between 8.3 and 10.4 is \( 10.4 - 8.3 = 2.1 \).
- The interval between 11.1 and 13.2 is \( 13.2 - 11.1 = 2.1 \).
- Filling in the blanks:
- Next mark after 8.3: \( 8.3 + 1.05 = 9.35 \) (midpoint of 8.3 and 10.4).
- Next mark after 9.35: \( 9.35 + 1.05 = 10.4 \) (already given).
- Next mark after 10.4: \( 11.1 \) (already given).
- Next mark after 11.1: \( 11.1 + 1.05 = 12.15 \).
- Next mark after 12.15: \( 13.2 \) (already given).

Completed number line:
```
<---|---|---|---|---|---|--->
8.3 9.35 10.4 11.1 12.15 13.2
```

Comparison: \( 8.3 \, ? \, 11.1 \)
- Since 8.3 is to the left of 11.1 on the number line, \( 8.3 < 11.1 \).

Answer for 3:
\[
\boxed{<}
\]

---

#### 4.
Number line:
```
<---|---|---|---|---|---|--->
1.2 2.1 3.9
```
- The interval between 1.2 and 2.1 is \( 2.1 - 1.2 = 0.9 \).
- The interval between 2.1 and 3.9 is \( 3.9 - 2.1 = 1.8 \).
- Filling in the blanks:
- Next mark after 1.2: \( 1.2 + 0.9 = 2.1 \) (already given).
- Next mark after 2.1: \( 2.1 + 0.9 = 3.0 \).
- Next mark after 3.0: \( 3.0 + 0.9 = 3.9 \) (already given).
- Next mark after 3.9: \( 3.9 + 0.9 = 4.8 \).

Completed number line:
```
<---|---|---|---|---|---|--->
1.2 2.1 3.0 3.9 4.8
```

Comparison: \( 2.1 \, ? \, 3.9 \)
- Since 2.1 is to the left of 3.9 on the number line, \( 2.1 < 3.9 \).

Answer for 4:
\[
\boxed{<}
\]

---

#### 5.
Number line:
```
<---|---|---|---|---|---|--->
2 2.2 3 3.6 3.8
```
- The interval between 2 and 2.2 is \( 2.2 - 2 = 0.2 \).
- The interval between 3 and 3.6 is \( 3.6 - 3 = 0.6 \).
- Filling in the blanks:
- Next mark after 2.2: \( 2.2 + 0.2 = 2.4 \).
- Next mark after 2.4: \( 2.4 + 0.2 = 2.6 \).
- Next mark after 2.6: \( 2.6 + 0.2 = 2.8 \).
- Next mark after 2.8: \( 3.0 \) (already given).
- Next mark after 3.0: \( 3.2 \).
- Next mark after 3.2: \( 3.4 \).
- Next mark after 3.4: \( 3.6 \) (already given).

Completed number line:
```
<---|---|---|---|---|---|---|---|---|--->
2 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
```

Comparison: \( 3.6 \, ? \, 2.2 \)
- Since 3.6 is to the right of 2.2 on the number line, \( 3.6 > 2.2 \).

Answer for 5:
\[
\boxed{>}
\]

---

#### 6.
Number line:
```
<---|---|---|---|---|---|--->
10.5 11.5 12
```
- The interval between 10.5 and 11.5 is \( 11.5 - 10.5 = 1.0 \).
- The interval between 11.5 and 12 is \( 12 - 11.5 = 0.5 \).
- Filling in the blanks:
- Next mark after 10.5: \( 10.5 + 0.5 = 11.0 \).
- Next mark after 11.0: \( 11.5 \) (already given).
- Next mark after 11.5: \( 12.0 \) (already given).
- Next mark after 12.0: \( 12.5 \).

Completed number line:
```
<---|---|---|---|---|---|--->
10.5 11.0 11.5 12.0 12.5
```

Comparison: \( 10.5 \, ? \, 11.5 \)
- Since 10.5 is to the left of 11.5 on the number line, \( 10.5 < 11.5 \).

Answer for 6:
\[
\boxed{<}
\]

---

#### 7.
Number line:
```
<---|---|---|---|---|---|---|--->
0.7 1 1.3 1.4
```
- The interval between 0.7 and 1 is \( 1 - 0.7 = 0.3 \).
- The interval between 1 and 1.3 is \( 1.3 - 1 = 0.3 \).
- The interval between 1.3 and 1.4 is \( 1.4 - 1.3 = 0.1 \).
- Filling in the blanks:
- Next mark after 0.7: \( 0.7 + 0.3 = 1.0 \).
- Next mark after 1.0: \( 1.3 \) (already given).
- Next mark after 1.3: \( 1.4 \) (already given).
- Next mark after 1.4: \( 1.4 + 0.1 = 1.5 \).
- Next mark after 1.5: \( 1.5 + 0.1 = 1.6 \).

Completed number line:
```
<---|---|---|---|---|---|---|--->
0.7 1.0 1.3 1.4 1.5 1.6
```

Comparison: \( 0.7 \, ? \, 1.3 \)
- Since 0.7 is to the left of 1.3 on the number line, \( 0.7 < 1.3 \).

Answer for 7:
\[
\boxed{<}
\]

---

Final Answers:

1. \( \boxed{<} \)
2. \( \boxed{>} \)
3. \( \boxed{<} \)
4. \( \boxed{<} \)
5. \( \boxed{>} \)
6. \( \boxed{<} \)
7. \( \boxed{<} \)