Worksheet for practicing multiplication by tenths and hundredths using number machines.

Let's solve each of the number machines step by step. Each machine multiplies the input number by a given decimal (tenths or hundredths). We'll use the rule:

> When multiplying by decimals, you can think of it as:
> - Multiply the whole numbers first.
> - Then count the total number of decimal places in the factors and place the decimal point accordingly.

We’ll go through each section one at a time.

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1) x 0.06

Given:
3 → 0.18 (since 3 × 0.06 = 0.18)

Now calculate the rest:

- 6 → 6 × 0.06 = 0.36 ✔
- 7 → 7 × 0.06 = 0.42
- 4 → 4 × 0.06 = 0.24
- 5 → 5 × 0.06 = 0.30
- 9 → 9 × 0.06 = 0.54
- 2 → 2 × 0.06 = 0.12

✔ All filled.

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2) x 0.5

Given:
0.3 → 0.15 (0.3 × 0.5 = 0.15)

Now:

- 6 → 6 × 0.5 = 3.0
- 0.7 → 0.7 × 0.5 = 0.35
- 4 → 4 × 0.5 = 2.0
- 5 → 5 × 0.5 = 2.5
- 0.9 → 0.9 × 0.5 = 0.45
- 2 → 2 × 0.5 = 1.0

✔ Done.

---

3) x 0.02

Given:
7 → 0.14 (7 × 0.02 = 0.14)

Now:

- ? → 0.04 → Let’s find input: 0.04 ÷ 0.02 = 2
- 3 → 3 × 0.02 = 0.06
- 9 → 9 × 0.02 = 0.18
- ? → 0.12 → 0.12 ÷ 0.02 = 6
- ? → 0.16 → 0.16 ÷ 0.02 = 8
- 4 → 4 × 0.02 = 0.08

So fill in:

- Input for 0.04: 2
- 3 → 0.06
- 9 → 0.18
- Input for 0.12: 6
- Input for 0.16: 8
- 4 → 0.08

✔ Complete.

---

4) x 0.8

Given:
? → 6.4 → So input = 6.4 ÷ 0.8 = 8

Also:
4 → ? → 4 × 0.8 = 3.2

Then:
? → 8.0 → 8.0 ÷ 0.8 = 10

Now:

- 7 → 7 × 0.8 = 5.6
- ? → 0.48 → 0.48 ÷ 0.8 = 0.6
- ? → 0.72 → 0.72 ÷ 0.8 = 0.9

So inputs and outputs:

- 5 → ?
- 5 × 0.8 = 4.0
- 4 → 3.2
- 10 → 8.0
- 7 → 5.6
- 0.6 → 0.48
- 0.9 → 0.72

Wait — check what’s listed:

Original list:

```
5 → ?
→ 6.4 → so input is 8
4 → ?
→ 8.0 → input is 10
7 → ?
→ 0.48 → input 0.6
→ 0.72 → input 0.9
```

So fill in:

- 5 → 5 × 0.8 = 4.0
- 4 → 4 × 0.8 = 3.2
- 7 → 7 × 0.8 = 5.6
- 0.6 → 0.48
- 0.9 → 0.72

But the output 6.4 comes from input 8, and 8.0 from input 10.

So we need to write:

- 5 → 4.0
- 4 → 3.2
- 7 → 5.6
- 0.6 → 0.48
- 0.9 → 0.72

And also, since 8 → 6.4 and 10 → 8.0, those are already implied.

✔ Done.

---

5) x 0.04

Given:
? → 0.28 → input = 0.28 ÷ 0.04 = 7
? → 0.36 → input = 0.36 ÷ 0.04 = 9

Now:

- 2 → 2 × 0.04 = 0.08
- 5 → 5 × 0.04 = 0.20
- 6 → 6 × 0.04 = 0.24
- ? → 0.12 → input = 0.12 ÷ 0.04 = 3
- ? → 0.16 → input = 0.16 ÷ 0.04 = 4

So:

- 2 → 0.08
- 5 → 0.20
- 7 → 0.28
- 9 → 0.36
- 6 → 0.24
- 3 → 0.12
- 4 → 0.16

✔ Complete.

---

6) x 0.01

Given:
? → 0.05 → input = 0.05 ÷ 0.01 = 5
? → 0.08 → input = 0.08 ÷ 0.01 = 8

Now:

- 3 → 3 × 0.01 = 0.03
- 7 → 7 × 0.01 = 0.07
- 6 → 6 × 0.01 = 0.06
- ? → 0.01 → input = 0.01 ÷ 0.01 = 1
- ? → 0.09 → input = 0.09 ÷ 0.01 = 9

So:

- 3 → 0.03
- 5 → 0.05
- 7 → 0.07
- 8 → 0.08
- 6 → 0.06
- 1 → 0.01
- 9 → 0.09

✔ Done.

---

7) x 0.07

Given:
? → 0.21 → input = 0.21 ÷ 0.07 = 3

Also:
? → 0.63 → input = 0.63 ÷ 0.07 = 9

? → 0.49 → input = 0.49 ÷ 0.07 = 7

Now:

- 5 → 5 × 0.07 = 0.35
- 2 → 2 × 0.07 = 0.14
- 6 → 6 × 0.07 = 0.42
- 4 → 4 × 0.07 = 0.28

So:

- 5 → 0.35
- 3 → 0.21
- 2 → 0.14
- 9 → 0.63
- 7 → 0.49
- 6 → 0.42
- 4 → 0.28

✔ Complete.

---

8) x 0.3

Given:
6 → ? → 6 × 0.3 = 1.8

? → 2.4 → input = 2.4 ÷ 0.3 = 8

? → 0.12 → input = 0.12 ÷ 0.3 = 0.4

? → 0.18 → input = 0.18 ÷ 0.3 = 0.6

Now:

- 9 → 9 × 0.3 = 2.7
- 0.8 → 0.8 × 0.3 = 0.24
- 0.5 → 0.5 × 0.3 = 0.15

So:

- 6 → 1.8
- 8 → 2.4
- 0.4 → 0.12
- 0.6 → 0.18
- 9 → 2.7
- 0.8 → 0.24
- 0.5 → 0.15

✔ Done.

---

9) x 0.09

Given:
? → 0.18 → input = 0.18 ÷ 0.09 = 2

5 → ? → 5 × 0.09 = 0.45

8 → ? → 8 × 0.09 = 0.72

3 → ? → 3 × 0.09 = 0.27

? → 0.36 → input = 0.36 ÷ 0.09 = 4

? → 0.54 → input = 0.54 ÷ 0.09 = 6

So:

- 2 → 0.18
- 5 → 0.45
- 8 → 0.72
- 3 → 0.27
- 4 → 0.36
- 6 → 0.54

✔ Complete.

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✔ Final Answer Summary:

#### 1) x 0.06
- 7 → 0.42
- 4 → 0.24
- 5 → 0.30
- 9 → 0.54
- 2 → 0.12

#### 2) x 0.5
- 6 → 3.0
- 0.7 → 0.35
- 4 → 2.0
- 5 → 2.5
- 0.9 → 0.45
- 2 → 1.0

#### 3) x 0.02
- 2 → 0.04
- 3 → 0.06
- 9 → 0.18
- 6 → 0.12
- 8 → 0.16
- 4 → 0.08

#### 4) x 0.8
- 5 → 4.0
- 4 → 3.2
- 7 → 5.6
- 0.6 → 0.48
- 0.9 → 0.72

(Also: 8 → 6.4, 10 → 8.0)

#### 5) x 0.04
- 2 → 0.08
- 5 → 0.20
- 7 → 0.28
- 9 → 0.36
- 6 → 0.24
- 3 → 0.12
- 4 → 0.16

#### 6) x 0.01
- 3 → 0.03
- 5 → 0.05
- 7 → 0.07
- 8 → 0.08
- 6 → 0.06
- 1 → 0.01
- 9 → 0.09

#### 7) x 0.07
- 5 → 0.35
- 3 → 0.21
- 2 → 0.14
- 9 → 0.63
- 7 → 0.49
- 6 → 0.42
- 4 → 0.28

#### 8) x 0.3
- 6 → 1.8
- 8 → 2.4
- 0.4 → 0.12
- 0.6 → 0.18
- 9 → 2.7
- 0.8 → 0.24
- 0.5 → 0.15

#### 9) x 0.09
- 2 → 0.18
- 5 → 0.45
- 8 → 0.72
- 3 → 0.27
- 4 → 0.36
- 6 → 0.54

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✔ Explanation:

Each problem involves multiplying by a decimal (tenths or hundredths). The key idea is:

> Multiply as if they were whole numbers, then count decimal places.

For example:
- 7 × 0.06 = 7 × 6 = 42 → now 0.06 has 2 decimal places → so answer is 0.42
- 0.7 × 0.5 = 7 × 5 = 35 → two decimals → 0.35

You can also use the rule:
> Multiplying by 0.1 moves the decimal one place left.
> Multiplying by 0.01 moves it two places left.
> So multiplying by 0.06 = 6 × 0.01 → move two places left and multiply by 6.

This method helps avoid errors.

Let me know if you'd like this formatted into a printable sheet!