Educational worksheet for practicing decimal numbers on number lines.

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`

- From 0.2 to 0.4 is an increase of 0.2.
- So, the pattern is increasing by 0.2 each time.
- Let’s list them:
- 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.

Look at known values:

- 7 → ?
- ? → 7.42
- Then more steps to 8.05, 8.26

Let’s see the gap from 7.42 to 8.05 = 8.05 – 7.42 = 0.63

But that’s over two intervals (from 7.42 to next blank to 8.05), so maybe not equal spacing.

Wait — perhaps look at 7.42 and 8.05, difference = 0.63
Then from 8.05 to 8.26 = 0.21

That doesn’t suggest a consistent pattern.

Wait — let’s count the total number of segments.

There are 8 segments (9 points). But we only have some values.

List positions:

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

So we have:

From position 1 to 3: 7 → 7.42 → difference = 0.42 over 2 steps → each step = 0.21

Try that:

- Step 1: 7
- Step 2: 7 + 0.21 = 7.21
- Step 3: 7.42 ✔
- Step 4: 7.42 + 0.21 = 7.63
- Step 5: 7.63 + 0.21 = 7.84
- Step 6: 7.84 + 0.21 = 8.05 ✔
- Step 7: 8.05 + 0.21 = 8.26 ✔
- Step 8: 8.26 + 0.21 = 8.47
- Step 9: 8.47 + 0.21 = 8.68

So all missing values:

- 7.21, 7.63, 7.84, 8.47, 8.68

Wait — but the blanks are:

- After 7: 7.21
- After 7.42: 7.63
- Then next blank: 7.84
- Then 8.05 (given)
- Then 8.26 (given)
- Then blanks: 8.47, 8.68

So blanks:
→ 7.21, 7.63, 7.84, 8.47, 8.68

✔ Answer: 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
- So likely increment of 0.1

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

Missing: 4.3, 4.4, 4.7, 4.8

✔ Answer: 4.3, 4.4, 4.7, 4.8

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

Let’s analyze:

- 2.65 → ? → 2.95

Difference: 2.95 – 2.65 = 0.30 over 2 steps → each step = 0.15

So:
- 2.65
- 2.65 + 0.15 = 2.80
- 2.95 ✔

Now: 2.95 → 3.1 → difference = 0.15 → so again, 0.15 per step?

But wait: 2.95 to 3.1 is 0.15, so yes!

Then:
- 3.1 → next: 3.1 + 0.15 = 3.25
- Next: 3.25 + 0.15 = 3.40
- Next: 3.40 + 0.15 = 3.55 ✔

So the sequence is:
- 2.65
- 2.80
- 2.95
- 3.1
- 3.25
- 3.40
- 3.55

Blanks:
- After 2.65: 2.80
- After 2.95: already 3.1 (given)
- Then after 3.1: 3.25
- Then 3.40

So missing: 2.80, 3.25, 3.40

✔ Answer: 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 can find the pattern.

Look at known values:

- 5.13 → C → 5.41 → difference = 5.41 – 5.13 = 0.28 over 2 steps → so each step = 0.14

Check:
- 5.13 + 0.14 = 5.27 → so C = 5.27
- 5.27 + 0.14 = 5.41 ✔

Now, 5.41 → 5.55 = 0.14 → yes! So constant increment of 0.14

So every step increases by 0.14

Now find A, B, C:

- C = 5.13 + 0.14 = 5.27
- A is after 5.55: 5.55 → A → 5.83

5.83 – 5.55 = 0.28 → over 2 steps → each 0.14

So:
- 5.55 + 0.14 = 5.69
- 5.69 + 0.14 = 5.83 → so A = 5.69

Next: 5.97 → B → 6.25

6.25 – 5.97 = 0.28 → over 2 steps → each 0.14

So:
- 5.97 + 0.14 = 6.11 → so B = 6.11

✔ Answers:
- 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

Look at the values:

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

From 9.02 to 9.03 = +0.01
9.03 to 9.05 = +0.02 → not consistent?

Wait — maybe check spacing.

But 9.03 → 9.05 = 0.02 → but if it's uniform, maybe not.

Wait — perhaps the pattern is 0.01 increments?

Let’s assume each tick is 0.01 apart.

So:

- Start at 9
- Then Q = 9.01 (since 9 → 9.01 → 9.02)
- Then 9.02 → 9.03 → 9.04 → R → 9.05 → ...

So:
- R should be at 9.04? But it's shown after 9.03 and before 9.05 → so R = 9.04

Then:
- 9.06 → 9.07 → P → what's next?

P is after 9.07 → so if pattern continues, P = 9.08

But is the spacing consistent?

Let’s list:

- 9.00
- Q = 9.01
- 9.02
- 9.03
- R = 9.04
- 9.05
- 9.06
- 9.07
- P = 9.08

Yes, seems like every tick is 0.01 apart.

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

✔ Answers:
- 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`

Find pattern.

From 1.9 to 2.01 = +0.11

But 1.9 → 2.01 is one step? Or two?

Wait — there's a gap: 1.9 → 2.01 → X → 2.23

So:

- 1.9 → 2.01 = +0.11
- 2.01 → X → 2.23

Let’s suppose the pattern is 0.11 per step?

Then:
- 2.01 + 0.11 = 2.12 → X = 2.12
- 2.12 + 0.11 = 2.23 ✔

Then:
- 2.23 → Z → 2.45

2.45 – 2.23 = 0.22 → over 2 steps → each 0.11

So:
- 2.23 + 0.11 = 2.34 → Z = 2.34
- 2.34 + 0.11 = 2.45 ✔

Then:
- 2.45 → Y → 2.67

2.67 – 2.45 = 0.22 → over 2 steps → each 0.11

So:
- 2.45 + 0.11 = 2.56 → Y = 2.56
- 2.56 + 0.11 = 2.67 ✔

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

✔ Answers:
- 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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Let me know if you'd like this formatted as a printable answer sheet!