Compare decimals on a number line worksheet from Math Monks.

Let's solve each part of this worksheet step by step.

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Task:

Complete the number lines and compare the given decimal numbers using > or <.

We'll:
1. Fill in the missing numbers on the number lines.
2. Compare the two decimals given at the end of each line.

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1. Number Line: 0.8 → 2.9

Given points:
- 0.8, 1.1, 2, 2.3, 2.9

We need to fill in the blanks between them.

Let’s examine the spacing:

From 0.8 to 1.1: difference = 0.3 → likely divided into 3 equal parts? But we have only one blank before 1.1.

Wait — let's count the tick marks.

The number line has ticks at:

- First blank
- Second blank
- 0.8
- 1.1
- Blank
- Blank
- 2
- 2.3
- Blank
- 2.9

So there are 10 tick marks total (including labeled ones).

Let’s assume the number line goes from 0 to 3, with even spacing.

But let’s calculate the interval between ticks.

From 0.8 to 1.1 is 0.3 → 1 interval → so each tick is 0.3 apart?

But that can’t be because 0.8 to 1.1 is 0.3, and then next tick after 1.1 would be 1.4, then 1.7, 2.0, 2.3, etc.

Let’s test that:

- 0.8
- 1.1 (next)
- 1.4
- 1.7
- 2.0
- 2.3
- 2.6
- 2.9

But we have two blanks after 1.1, then 2, then 2.3, then a blank, then 2.9.

So:

- After 1.1 → blank → blank → 2

So if 1.1 → ? → ? → 2

That’s 3 intervals → total distance = 0.9 → each interval = 0.3

So:
- 1.1 + 0.3 = 1.4
- 1.4 + 0.3 = 1.7
- 1.7 + 0.3 = 2.0 ✔

Then 2 → 2.3 → 2.6 → 2.9

So the blanks:

- Before 0.8: 0.5 (since 0.8 - 0.3 = 0.5), then 0.2?
Wait — let's go left.

We have two blanks before 0.8.

If spacing is 0.3, then:

- Blank1: 0.5
- Blank2: 0.2
- Then 0.8

Yes!

And after 2.9: no blank, but it ends.

Now list all:

- □, □, 0.8, 1.1, □, □, 2, 2.3, □, 2.9

Fill in:

- 0.2, 0.5, 0.8, 1.1, 1.4, 1.7, 2.0, 2.3, 2.6, 2.9

So blanks:
1. 0.2
2. 0.5
3. 1.4
4. 1.7
5. 2.6

Now compare: 0.8 ___ 2.9

Clearly: 0.8 < 2.9

✔ Answer: 0.8 < 2.9

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2. Number Line: 4.6 → 6.6 → 7.1

Points: 4.6, then blanks, then 6.6, then 7.1

Blanks: □, 4.6, □, □, □, 6.6, 7.1

So from 4.6 to 6.6 is 2.0 → how many intervals?

Between 4.6 and 6.6: three blanks → so four intervals?

Wait: positions:

- □, 4.6, □, □, □, 6.6, 7.1

So from 4.6 to 6.6: 4 intervals? Let's count:

After 4.6: three blanks, then 6.6 → so 4 segments

Distance: 6.6 - 4.6 = 2.0 → each segment = 2.0 / 4 = 0.5

So:

- 4.6 + 0.5 = 5.1
- 5.1 + 0.5 = 5.6
- 5.6 + 0.5 = 6.1
- 6.1 + 0.5 = 6.6 ✔

Now before 4.6: one blank

So previous tick: 4.6 - 0.5 = 4.1

After 7.1: nothing, but 7.1 is last.

So blanks:

- 4.1, 4.6, 5.1, 5.6, 6.1, 6.6, 7.1

Now compare: 6.6 ___ 4.6

6.6 > 4.6 → 6.6 > 4.6

✔ Answer: 6.6 > 4.6

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3. Number Line: 8.3 → 11.1 → 13.2

Points: 8.3, then two blanks, then 10.4, 11.1, then two blanks, then 13.2

So:

- 8.3, □, □, 10.4, 11.1, □, □, 13.2

Let’s find spacing.

From 8.3 to 10.4: difference = 2.1

Number of intervals: from 8.3 to first blank → second blank → 10.4 → so 3 intervals

So each interval = 2.1 / 3 = 0.7

So:

- 8.3 + 0.7 = 9.0
- 9.0 + 0.7 = 9.7
- 9.7 + 0.7 = 10.4 ✔

Now from 11.1 to 13.2: difference = 2.1

Two blanks after 11.1 → so three intervals? Wait:

Positions: 11.1, □, □, 13.2 → two intervals

So 2.1 / 2 = 1.05 per interval

So:

- 11.1 + 1.05 = 12.15
- 12.15 + 1.05 = 13.2 ✔

Now check if consistent? The spacing changed? That’s possible.

But wait — is the whole line evenly spaced?

From 8.3 to 10.4: 2.1 over 3 steps → 0.7

From 10.4 to 11.1: 0.7 → yes! So maybe the spacing is 0.7 throughout?

Check: 10.4 → 11.1 = 0.7 → yes!

Then 11.1 → ? → ? → 13.2

If spacing is 0.7:

- 11.1 + 0.7 = 11.8
- 11.8 + 0.7 = 12.5
- 12.5 + 0.7 = 13.2 ✔

But we only have two blanks after 11.1 → so 11.8 and 12.5 → then 13.2

Yes.

So full sequence:

- 8.3, 9.0, 9.7, 10.4, 11.1, 11.8, 12.5, 13.2

Now compare: 8.3 ___ 11.1

8.3 < 11.1 → 8.3 < 11.1

✔ Answer: 8.3 < 11.1

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4. Number Line: 2.1 → 3.9

Points: □, 1.2, 2.1, □, 3.9, □, □

So:

- □, 1.2, 2.1, □, 3.9, □, □

From 1.2 to 2.1 = 0.9 → one interval → so spacing = ?

But 1.2 to 2.1: difference = 0.9 → one space → so each interval = 0.9?

Then:

- Before 1.2: 1.2 - 0.9 = 0.3
- After 2.1: 2.1 + 0.9 = 3.0
- Then 3.0 + 0.9 = 3.9 ✔
- Then 3.9 + 0.9 = 4.8
- Then 4.8 + 0.9 = 5.7

So blanks:

- 0.3, 1.2, 2.1, 3.0, 3.9, 4.8, 5.7

Compare: 2.1 ___ 3.9

2.1 < 3.9 → 2.1 < 3.9

✔ Answer: 2.1 < 3.9

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5. Number Line: 2.2 → 3.8

Points: 2, 2.2, □, □, □, 3, □, □, 3.6, 3.8

So:

- 2, 2.2, □, □, □, 3, □, □, 3.6, 3.8

From 2 to 2.2 = 0.2 → one interval → so spacing = 0.2?

Then:

- 2.2 → 2.4 → 2.6 → 2.8 → 3.0 → 3.2 → 3.4 → 3.6 → 3.8

But we have:

- 2, 2.2, □, □, □, 3, □, □, 3.6, 3.8

So:

- After 2.2: 2.4, 2.6, 2.8 → then 3.0
- Then 3.2, 3.4 → then 3.6, 3.8

So blanks:

- 2.4, 2.6, 2.8, 3.2, 3.4

Now compare: 3.6 ___ 2.2

3.6 > 2.2 → 3.6 > 2.2

✔ Answer: 3.6 > 2.2

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6. Number Line: 10.5 → 11.5 → 12

Points: □, 10.5, □, 11.5, 12, □

So:

- □, 10.5, □, 11.5, 12, □

From 10.5 to 11.5 = 1.0 → two intervals → so each = 0.5

So:

- Before 10.5: 10.5 - 0.5 = 10.0
- After 10.5: 10.5 + 0.5 = 11.0
- Then 11.5, 12.0, then 12.5

So blanks:

- 10.0, 10.5, 11.0, 11.5, 12, 12.5

Compare: 10.5 ___ 11.5

10.5 < 11.5 → 10.5 < 11.5

✔ Answer: 10.5 < 11.5

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7. Number Line: 0.7 → 1.3

Points: 0.7, □, □, 1, □, □, 1.3, 1.4, □, □, □

So:

- 0.7, □, □, 1, □, □, 1.3, 1.4, □, □, □

From 0.7 to 1 = 0.3 → two intervals → so each = 0.15?

But 1 to 1.3 = 0.3 → also two intervals → 0.15 each?

Try:

- 0.7 → 0.85 → 1.0 → 1.15 → 1.3 → 1.4 → 1.55 → 1.7 → 1.85

But we have:

- 0.7, □, □, 1, □, □, 1.3, 1.4, □, □, □

So from 0.7 to 1: two intervals → so spacing = (1 - 0.7)/2 = 0.3/2 = 0.15

So:

- 0.7 + 0.15 = 0.85
- 0.85 + 0.15 = 1.0

Then from 1 to 1.3: three intervals? No — 1 → □ → □ → 1.3 → two intervals

So 1.3 - 1 = 0.3 → two intervals → 0.15 each

So:

- 1 + 0.15 = 1.15
- 1.15 + 0.15 = 1.3

Then 1.3 → 1.4 → 0.1 → so spacing changes?

Wait — 1.3 to 1.4 is 0.1 → then next blank?

But earlier spacing was 0.15 → now 0.1?

Possibly not uniform.

Wait — look at 1.3 to 1.4: just one interval → then three more blanks.

But perhaps the spacing is 0.1 after 1.3?

But from 1.3 to 1.4 = 0.1 → so maybe spacing is 0.1?

But earlier from 0.7 to 1: 0.3 in two steps → 0.15

Inconsistent.

Alternatively, maybe spacing is 0.1 throughout?

Check:

From 0.7 to 1 = 0.3 → should be 3 intervals → but we have only two blanks → so three tick marks: 0.7, ?, ?, 1 → so 3 intervals

So if spacing is 0.1:

- 0.7 → 0.8 → 0.9 → 1.0

Yes!

Then 1.0 → ? → ? → 1.3 → so 3 intervals → 0.3 → each 0.1

So:

- 1.0 → 1.1 → 1.2 → 1.3

Then 1.3 → 1.4 → 0.1

Then 1.4 → 1.5 → 1.6 → 1.7

So blanks:

- 0.8, 0.9, 1.1, 1.2, 1.5, 1.6, 1.7

Full line:

- 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7

Perfect — all spaced by 0.1

Now compare: 0.7 ___ 1.3

0.7 < 1.3 → 0.7 < 1.3

✔ Answer: 0.7 < 1.3

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✔ Final Answers:

1. 0.8 < 2.9
2. 6.6 > 4.6
3. 8.3 < 11.1
4. 2.1 < 3.9
5. 3.6 > 2.2
6. 10.5 < 11.5
7. 0.7 < 1.3

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✔ Completed Number Lines (for reference):

1. 0.2, 0.5, 0.8, 1.1, 1.4, 1.7, 2.0, 2.3, 2.6, 2.9
2. 4.1, 4.6, 5.1, 5.6, 6.1, 6.6, 7.1
3. 8.3, 9.0, 9.7, 10.4, 11.1, 11.8, 12.5, 13.2
4. 0.3, 1.2, 2.1, 3.0, 3.9, 4.8, 5.7
5. 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8
6. 10.0, 10.5, 11.0, 11.5, 12, 12.5
7. 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7

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All problems solved! 🎉