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’ll analyze each number line and determine the pattern or interval between marked numbers to find the missing values.

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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 look at known points:

- 7 → ? → 7.42 → ? → ? → 8.05 → 8.26 → ? → ?

First, from 7 to 7.42 is a jump of 0.42 over two steps? Wait — let's count the intervals.

There are 9 positions, but only some are labeled. Let's label the positions:

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

Now, check differences:

From position 3 (7.42) to position 6 (8.05):
8.05 - 7.42 = 0.63 over 3 steps → so increment = 0.63 / 3 = 0.21

Check if this fits with earlier:

From 7 to 7.42: difference = 0.42 over 2 steps → 0.42 / 2 = 0.21 ✔

So, common interval = 0.21

Now fill in:

- Position 1: 7.00
- Position 2: 7.00 + 0.21 = 7.21
- Position 3: 7.42 ✔
- Position 4: 7.42 + 0.21 = 7.63
- Position 5: 7.63 + 0.21 = 7.84
- Position 6: 8.05 ✔
- Position 7: 8.26 ✔
- Position 8: 8.26 + 0.21 = 8.47
- Position 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
So likely increments of 0.1

Let’s list:

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

So missing: 4.3, 4.4, 4.7, 4.8

✔ Missing numbers: 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 look at known values:

- 2.65 → ? → 2.95 → 3.1 → ? → ? → 3.55

From 2.65 to 2.95: difference = 0.30 over 2 steps → 0.30 / 2 = 0.15

Check next: 2.95 to 3.1 = 0.15 → yes! So increment = 0.15

Now fill:

- 2.65
- 2.65 + 0.15 = 2.80
- 2.95 ✔
- 3.10 ✔
- 3.10 + 0.15 = 3.25
- 3.25 + 0.15 = 3.40
- 3.40 + 0.15 = 3.55 ✔

So missing: 2.80, 3.25, 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`

Let’s identify the pattern.

Look at the known points:

- 5.13 → C → 5.41 → 5.55 → A → 5.83 → 5.97 → B → 6.25 → 6.39 → 6.53

Check differences:

- 5.13 to 5.41 = 0.28 → over 2 steps? But there's one gap: C is between 5.13 and 5.41

So: 5.13 → C → 5.41 → difference = 0.28 → over 2 intervals → each step = 0.14?

Wait: from 5.13 to 5.41 is 0.28, and only one space in between → so it's one interval.

So C = (5.13 + 5.41)/2? No — not necessarily equally spaced unless we assume that.

But let’s check other intervals:

- 5.41 to 5.55 = 0.14
- 5.55 to 5.83 = 0.28 → wait, not consistent

Wait — maybe look at larger jumps.

Try to see if all are spaced by 0.14?

Let’s test:

- 5.13
- 5.13 + 0.14 = 5.27 → C?
- 5.27 + 0.14 = 5.41 ✔
- 5.41 + 0.14 = 5.55 ✔
- 5.55 + 0.14 = 5.69 → A?
- 5.69 + 0.14 = 5.83 ✔
- 5.83 + 0.14 = 5.97 ✔
- 5.97 + 0.14 = 6.11 → B?
- 6.11 + 0.14 = 6.25 ✔
- 6.25 + 0.14 = 6.39 ✔
- 6.39 + 0.14 = 6.53 ✔

Perfect! All steps are +0.14

So:

- C = 5.13 + 0.14 = 5.27
- A = 5.55 + 0.14 = 5.69
- B = 5.97 + 0.14 = 6.11

✔ 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`

Let’s look at knowns:

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

From 9.02 to 9.03 = +0.01
Then 9.03 → R → 9.05 → so R must be 9.04 (since 9.03 + 0.01 = 9.04, then +0.01 = 9.05)

Similarly:

- 9.05 → 9.06 → 9.07 → P → likely P = 9.08?

Now what about Q?

9 → Q → 9.02

Difference: 9.02 - 9 = 0.02 → over one step → so Q = 9 + 0.01 = 9.01

Because if it's uniform, spacing = 0.01

Let’s verify:

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

Yes, all steps are +0.01

So:

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

✔ 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`

Let’s find the pattern.

Known points:

- 1.9 → 2.01 → X → 2.23 → Z → 2.45 → Y → 2.67

Check differences:

- 1.9 to 2.01 = +0.11
- 2.01 to X → ?
- X to 2.23 → ?
- 2.23 to Z → ?
- Z to 2.45 → ?
- 2.45 to Y → ?
- Y to 2.67 → ?

Let’s suppose equal spacing.

From 1.9 to 2.67: total = 2.67 - 1.9 = 0.77

How many intervals? Let's count the steps:

Positions:
1: 1.9
2: 2.01
3: X
4: 2.23
5: Z
6: 2.45
7: Y
8: 2.67

So 7 intervals between 8 points.

Total change: 0.77 over 7 steps → 0.77 / 7 = 0.11

So each step is +0.11

Let’s verify:

- 1.9
- 1.9 + 0.11 = 2.01 ✔
- 2.01 + 0.11 = 2.12 → X
- 2.12 + 0.11 = 2.23 ✔
- 2.23 + 0.11 = 2.34 → Z
- 2.34 + 0.11 = 2.45 ✔
- 2.45 + 0.11 = 2.56 → Y
- 2.56 + 0.11 = 2.67 ✔

Perfect!

So:

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

✔ 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) Letter values:

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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