Long Division With Decimals Worksheets | PDF - Free Printable

Let's solve each of the long division problems with decimals step by step. The goal is to find the quotient for each problem.

---

① 6 ÷ 9.8

We are dividing 9.8 ÷ 6

```
1.633...
_________
6 | 9.800
-6
---
3.8
-3.6
----
0.20
-0.18
-----
0.020
-0.018
-------
0.002...
```

So, 9.8 ÷ 6 = 1.633... ≈ 1.63 (rounded to two decimal places)

✔ Answer: 1.63

---

② 83 ÷ 814.50

We are dividing 814.50 ÷ 83

```
9.813...
___________
83 | 814.50
-747
------
67.5
-66.4
------
1.10
-0.83
------
0.270
-0.249
-------
0.021
```

So, 814.50 ÷ 83 ≈ 9.81

✔ Answer: 9.81

---

③ 5 ÷ 48.6

We are dividing 48.6 ÷ 5

```
9.72
________
5 | 48.60
-45
----
3.6
-3.5
----
0.10
-0.00
----
0.10 → bring down 0 → 10
-10
---
0
```

Wait — correction:

Actually:
- 48.6 ÷ 5

Step-by-step:
- 5 into 48 → 9 times → 9×5=45 → subtract → 3
- Bring down 6 → 36
- 5 into 36 → 7 times → 7×5=35 → remainder 1
- Add decimal point and 0 → 10
- 5 into 10 → 2 times → 2×5=10 → remainder 0

So: 9.72

✔ Answer: 9.72

---

④ 12 ÷ 141.84

Divide 141.84 ÷ 12

```
11.82
_________
12 | 141.84
-12
----
21
-12
----
9.8
-9.6
----
0.24
-0.24
----
0
```

So, 141.84 ÷ 12 = 11.82

✔ Answer: 11.82

---

⑤ 33 ÷ 166.44

Divide 166.44 ÷ 33

```
5.04
_________
33 | 166.44
-165
------
1.44
-1.32
------
0.12 → add 0 → 1.2
-1.32 → too big → so 0.04 × 33 = 1.32
So we have 5.04
```

Check: 33 × 5.04 = ?

33 × 5 = 165
33 × 0.04 = 1.32 → total = 166.32
But dividend is 166.44 → difference = 0.12 → not exact?

Wait — let's do it carefully:

```
5.043...
_________
33 | 166.44
-165
------
1.44
-1.32
------
0.120 → bring down 0 → 1.20
-1.32 → can't go → so 0 → next digit?
```

Wait — better:

After 1.44, we have:

- 33 into 144 → 4 times? No, we're at 1.44 → actually:

We already did:

- 33 × 5 = 165 → subtract from 166.44 → remainder 1.44
- Bring down 0 → 14.4
- 33 into 14.4 → 0 → place decimal → now consider 144 tenths?

Better method:

Do 166.44 ÷ 33

Convert to whole numbers: multiply numerator and denominator by 100:

→ 16644 ÷ 3300 → but easier to do long division:

```
5.043...
__________
33 | 166.44
-165
------
1.44
-1.32
------
0.120 → bring down 0 → 1.20 → wait, no — we have 1.44, then add decimal → 1.44 → then add 0 → 14.4
```

Wait — after 1.44, we bring down a 0 → 14.4 → but since we're past decimal, we’re in hundredths.

So:

- 33 into 144 (hundredths) → 4 times → 33×4=132 → 144−132=12 → remainder 12 hundredths → 0.12
- Then add another 0 → 120 thousandths
- 33 into 120 → 3 times → 33×3=99 → 120−99=21
- So quotient is 5.043...

But let’s check:

33 × 5.04 = 33×5 + 33×0.04 = 165 + 1.32 = 166.32
166.44 − 166.32 = 0.12 → so need more precision.

Now: 33 × 5.043 = ?

33 × 5.043 = 33 × (5 + 0.04 + 0.003) = 165 + 1.32 + 0.099 = 166.419

Close to 166.44 → difference 0.021

Next digit: 33 × 0.0006 = 0.0198 → close

So: 5.0436...

But likely we want rounded to two decimals.

So: 166.44 ÷ 33 ≈ 5.04 (since 33×5.04 = 166.32, and 166.44 − 166.32 = 0.12 → error)

Wait — perhaps better to compute directly:

Let’s divide:

```
5.043...
__________
33 | 166.44
-165
------
1.44
-1.32
------
0.120
-0.099
------
0.021 → so continue...
```

So: ≈ 5.043

But if rounding to two decimal places, look at third digit: 3 → round down → 5.04

✔ Answer: 5.04

---

⑥ 8 ÷ 124.30

Divide 124.30 ÷ 8

```
15.5375
__________
8 | 124.30
-8
---
44
-40
---
4.3
-4.0
----
0.30
-0.24
----
0.060
-0.056
----
0.004 → continue
```

Wait — let's do it properly:

- 8 into 12 → 1 → 1×8=8 → 12−8=4
- Bring down 4 → 44 → 8×5=40 → 44−40=4
- Bring down 3 → 43 → 8×5=40 → 43−40=3
- Bring down 0 → 30 → 8×3=24 → 30−24=6 → but we have decimal

Wait — better:

```
15.5375
__________
8 | 124.30
-8
---
44
-40
---
4.3
-4.0
----
0.30
-0.24
----
0.060
-0.056
----
0.004 → add 0 → 0.040
-0.040
----
0
```

Wait — after 0.30 → we have 0.30 → 8 into 30 → 3 → 3×8=24 → 30−24=6 → so 0.03 → but we need to track decimals.

Let’s align:

```
15.5375
__________
8 | 124.30
-8
---
44
-40
---
4.3
-4.0
----
0.30
-0.24
----
0.060
-0.056
----
0.0040 → add 0 → 0.040 → 8 into 40 → 5 → 5×8=40 → done
```

So: 15.5375

✔ Answer: 15.5375

But maybe round to two decimals? 15.54

But since it's exact, keep as 15.5375

But likely expect 15.54 or 15.5375

Let’s see: 8 × 15.5375 = ?

8 × 15 = 120
8 × 0.5 = 4 → total 124
8 × 0.0375 = 0.3 → total 124.3 → yes!

So 15.5375 is exact.

✔ Answer: 15.5375

---

⑦ 0.15 ÷ 0.75

This is 0.75 ÷ 0.15

To divide decimals, eliminate decimals by multiplying numerator and denominator by 100:

→ 75 ÷ 15 = 5

So, 0.75 ÷ 0.15 = 5

✔ Answer: 5

---

⑧ 27 ÷ 1581.37

Divide 1581.37 ÷ 27

```
58.569...
___________
27 | 1581.37
-135
------
231
-216
------
15.3
-13.5
------
1.80
-1.62
------
0.180
-0.162
------
0.018 → continue...
```

Let’s do step-by-step:

- 27 into 158 → 5 → 5×27=135 → 158−135=23
- Bring down 1 → 231 → 27×8=216 → 231−216=15
- Bring down 3 → 153 → 27×5=135 → 153−135=18
- Bring down 7 → 187 → 27×6=162 → 187−162=25 → wait — but we have decimal

Wait — dividend is 1581.37

So:

```
58.569...
___________
27 | 1581.37
-135
------
231
-216
------
15.3
-13.5
------
1.80
-1.62
------
0.180
-0.162
------
0.018 → add 0 → 0.180 → repeat?
```

Wait — let's write it clearly:

- 27 × 58 = 1566 → 1581.37 − 1566 = 15.37
- Now divide 15.37 ÷ 27 → 0.569...

So:

- 27 into 153 (tenths) → 5 → 5×27=135 → 153−135=18 → 18 tenths → 1.8
- Bring down 7 → 187 hundredths → 27×6=162 → 187−162=25 → 25 hundredths
- Add 0 → 250 → 27×9=243 → 250−243=7 → etc.

So quotient is 58.569...

Approximately: 58.57 (rounded to two decimals)

✔ Answer: 58.57

---

⑨ 31.3 ÷ 384.13

Divide 384.13 ÷ 31.3

To make it easier, eliminate decimals by multiplying both by 10:

→ 3841.3 ÷ 313

Now divide:

```
12.27...
__________
313 | 3841.3
-313
------
711
-626
------
85.3
-62.6
------
22.7 → add 0 → 227
-227
------
0
```

Wait — step-by-step:

- 313 into 384 → 1 → 1×313=313 → 384−313=71
- Bring down 1 → 711 → 313×2=626 → 711−626=85
- Bring down 3 → 853 → 313×2=626 → 853−626=227
- But we have decimal — so now: 227 → add decimal → 2270

Wait — original is 384.13 → so after 384.13, we have:

After 85.3 → 85.3 → 313 into 85.3 → 0 → place decimal → now 853 tenths

So:

- 313 into 853 → 2 → 2×313=626 → 853−626=227
- Bring down 0 → 2270 → 313×7=2191 → 2270−2191=79
- Bring down 0 → 790 → 313×2=626 → 790−626=164
- Continue...

So quotient is 12.27...

Check: 31.3 × 12.27 = ?

First: 31.3 × 12 = 375.6
31.3 × 0.27 = ?

31.3 × 0.2 = 6.26
31.3 × 0.07 = 2.191
Total = 6.26 + 2.191 = 8.451
Total = 375.6 + 8.451 = 384.051 → close to 384.13

Difference: 0.079 → so need slightly higher.

Try 12.28:

31.3 × 0.01 = 0.313 → so 31.3 × 12.28 = 384.051 + 0.313 = 384.364 → too high

So between 12.27 and 12.28

But 384.13 − 384.051 = 0.079 → so add 0.079 / 31.3 ≈ 0.0025 → so ≈ 12.2725

So ≈ 12.27

✔ Answer: 12.27

---

## ✔ Final Answers:

| Problem | Quotient |
|--------|----------|
| ① | 1.63 |
| ② | 9.81 |
| ③ | 9.72 |
| ④ | 11.82 |
| ⑤ | 5.04 |
| ⑥ | 15.5375 |
| ⑦ | 5 |
| ⑧ | 58.57 |
| ⑨ | 12.27 |

> Note: Some answers are exact (e.g., ⑦), others are rounded to two decimal places unless otherwise specified.

Let me know if you'd like the full long division steps shown for any one!