Decimals on a Number Line Worksheets - Free Printable

Let's solve the problem step by step.

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A) Fill in the missing decimal numbers on each number line

We need to determine the pattern or interval between the given numbers and then fill in the blanks accordingly.

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#### 1)
Number line:
`0.2` → `0.4` → `___` → `___` → `___` → `1.2`

- The difference between 0.2 and 0.4 is 0.2
- So, the numbers increase by 0.2 each time.
- Sequence:
- 0.2
- 0.4
- 0.6
- 0.8
- 1.0
- 1.2

✔ Missing numbers: 0.6, 0.8, 1.0

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#### 2)
Number line:
`7` → `___` → `7.42` → `___` → `___` → `8.05` → `8.26` → `___` → `___`

Let’s find the pattern.

We know:
- From 7 to 7.42 = +0.42
- But there’s one blank between 7 and 7.42 → so two intervals from 7 to 7.42?

Wait — positions:

Positions:
1: 7
2: ___
3: 7.42
4: ___
5: ___
6: 8.05
7: 8.26
8: ___
9: ___

So from 7 (pos 1) to 7.42 (pos 3): two steps → total change = 0.42 → each step = 0.21

So:
- Pos 2: 7 + 0.21 = 7.21
- Pos 3: 7.42 (given)
- Pos 4: 7.42 + 0.21 = 7.63
- Pos 5: 7.63 + 0.21 = 7.84
- Pos 6: 8.05 (given)

Check: 7.84 + 0.21 = 8.05 ✔

Now pos 7: 8.26 (given)
From 8.05 to 8.26 = +0.21 → yes, consistent!

So:
- Pos 8: 8.26 + 0.21 = 8.47
- Pos 9: 8.47 + 0.21 = 8.68

✔ Missing numbers: 7.21, 7.63, 7.84, 8.47, 8.68

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#### 3)
Number line:
`4.1` → `4.2` → `___` → `___` → `4.5` → `4.6` → `___` → `___`

From 4.1 to 4.2 = +0.1 → likely increasing by 0.1

So:
- 4.1
- 4.2
- 4.3
- 4.4
- 4.5
- 4.6
- 4.7
- 4.8

So missing numbers:
- After 4.2 → 4.3, 4.4
- After 4.6 → 4.7, 4.8

✔ Missing: 4.3, 4.4, 4.7, 4.8

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#### 4)
Number line:
`2.65` → `___` → `2.95` → `3.1` → `___` → `___` → `3.55`

We have:
- 2.65 → ? → 2.95 → 3.1 → ? → ? → 3.55

First, check from 2.65 to 2.95: difference = 0.30

But only one blank in between → so two steps? Wait: positions:

Pos 1: 2.65
Pos 2: ___
Pos 3: 2.95
Pos 4: 3.1
Pos 5: ___
Pos 6: ___
Pos 7: 3.55

So from 2.65 to 2.95: 2 steps → total 0.30 → each step = 0.15

So:
- Pos 2: 2.65 + 0.15 = 2.80
- Pos 3: 2.95 ✔

Now from 2.95 to 3.1: difference = 0.15 → one step → so next is 3.1

Then from 3.1 to 3.55: difference = 0.45 over 3 steps (positions 5,6,7)

Wait — after 3.1 (pos 4), we have:
- Pos 5: ?
- Pos 6: ?
- Pos 7: 3.55

So 3 steps from 3.1 to 3.55? No — 3.1 to 3.55 is 0.45, over two intervals (from pos 4 to 5, 5 to 6, 6 to 7) → three steps?

Wait: pos 4: 3.1
pos 5: ?
pos 6: ?
pos 7: 3.55

So 3 steps → total change = 0.45 → each step = 0.15

So:
- Pos 5: 3.1 + 0.15 = 3.25
- Pos 6: 3.25 + 0.15 = 3.40
- Pos 7: 3.55 ✔

But wait — is the increment consistent?

Earlier: 2.65 → 2.80 (+0.15), 2.80 → 2.95 (+0.15), 2.95 → 3.1 (+0.15), then 3.1 → 3.25 (+0.15), etc.

Yes! So every step is +0.15

So:
- Pos 2: 2.80
- Pos 5: 3.25
- Pos 6: 3.40

✔ Missing numbers: 2.80, 3.25, 3.40

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B) What decimal numbers do the letters represent?

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#### 1)
Number line:
`5.13` → C → `5.41` → `5.55` → A → `5.83` → `5.97` → B → `6.25` → `6.39` → `6.53`

We need to find values of A, B, C.

Look at the pattern.

From 5.13 to 5.41: difference = 0.28
But there’s one blank (C) in between → so two steps?

Wait: positions:
- 5.13
- C
- 5.41
- 5.55
- A
- 5.83
- 5.97
- B
- 6.25
- 6.39
- 6.53

So from 5.13 to 5.41: two steps → total 0.28 → each step = 0.14

So:
- C = 5.13 + 0.14 = 5.27

Now from 5.41 to 5.55 = +0.14 → yes

Next: 5.55 → A → 5.83

Two steps: 5.55 → A → 5.83 → difference = 0.28 → each step = 0.14

So:
- A = 5.55 + 0.14 = 5.69

Then: 5.83 → 5.97 = +0.14 → good

Then: 5.97 → B → 6.25

Difference: 6.25 - 5.97 = 0.28 → two steps → each = 0.14

So:
- B = 5.97 + 0.14 = 6.11

Check: 6.11 + 0.14 = 6.25 ✔

Now confirm all:
- 5.13 → 5.27 (+0.14) → 5.41 (+0.14) → 5.55 (+0.14) → 5.69 (+0.14) → 5.83 (+0.14) → 5.97 (+0.14) → 6.11 (+0.14) → 6.25 (+0.14) → 6.39 → 6.53

Wait — 6.25 to 6.39 = +0.14 → yes
6.39 to 6.53 = +0.14 → yes

Perfect.

✔ So:
- A = 5.69
- B = 6.11
- C = 5.27

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#### 2)
Number line:
`9` → Q → `9.02` → `9.03` → R → `9.05` → `9.06` → `9.07` → P

We can see:
- 9 → Q → 9.02 → 9.03 → R → 9.05 → 9.06 → 9.07 → P

From 9 to 9.02: difference = 0.02, with one blank (Q) → so two steps → each step = 0.01

So:
- Q = 9 + 0.01 = 9.01

Then:
- 9.02 → 9.03 → +0.01
- 9.03 → R → 9.05 → so R must be halfway?

Wait: 9.03 → R → 9.05 → difference = 0.02 → two steps → each = 0.01

So:
- R = 9.03 + 0.01 = 9.04

Then:
- 9.05 → 9.06 → 9.07 → then P

After 9.07, no number shown, but P is next.

Wait — last point is P, and before that is 9.07.

Is it increasing by 0.01?

Then:
- 9.07 → P → next would be 9.08?

But we don’t have a number after 9.07. However, since all previous steps are +0.01, and P is the next point, likely:
- P = 9.08

But let’s count positions:

- 9
- Q
- 9.02
- 9.03
- R
- 9.05
- 9.06
- 9.07
- P

So:
- 9 → Q → 9.02 → so Q = 9.01 ✔
- 9.03 → R → 9.05 → R = 9.04 ✔
- Then 9.07 → P → assuming same pattern, P = 9.08

But is there a gap? 9.07 to P — if the pattern continues, and the spacing is uniform, then yes.

But let’s check if there’s a jump.

Wait — from 9.06 to 9.07 = +0.01 → then P should be 9.08

✔ So:
- P = 9.08
- Q = 9.01
- R = 9.04

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#### 3)
Number line:
`1.9` → `2.01` → X → `2.23` → Z → `2.45` → Y → `2.67`

We need X, Y, Z.

First, from 1.9 to 2.01 = +0.11

Then 2.01 → X → 2.23

So two steps: 2.01 → X → 2.23 → difference = 0.22 → each step = 0.11

So:
- X = 2.01 + 0.11 = 2.12

Now: 2.23 → Z → 2.45 → difference = 0.22 → two steps → each = 0.11

So:
- Z = 2.23 + 0.11 = 2.34

Then: 2.45 → Y → 2.67 → difference = 0.22 → two steps → each = 0.11

So:
- Y = 2.45 + 0.11 = 2.56

Check:
- 1.9 → 2.01 (+0.11) → 2.12 (+0.11) → 2.23 (+0.11) → 2.34 (+0.11) → 2.45 (+0.11) → 2.56 (+0.11) → 2.67 (+0.11)

Perfect.

✔ So:
- X = 2.12
- Y = 2.56
- Z = 2.34

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✔ Final Answers

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A) Fill in the missing decimals

1) 0.6, 0.8, 1.0
2) 7.21, 7.63, 7.84, 8.47, 8.68
3) 4.3, 4.4, 4.7, 4.8
4) 2.80, 3.25, 3.40

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B) Values of letters

1)
- A = 5.69
- B = 6.11
- C = 5.27

2)
- P = 9.08
- Q = 9.01
- R = 9.04

3)
- X = 2.12
- Y = 2.56
- Z = 2.34

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