Worksheet on Dividing Decimals | Huge Number of Decimal Division Prob - Free Printable

Let's solve each problem step by step from the worksheet on dividing decimals.

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1. Divide the decimals by 10 or higher powers of 10:

When dividing by 10, 100, 1000, etc., you move the decimal point to the left by as many places as there are zeros in the divisor.

#### (a) $ 37.4 \div 10 $
- Move decimal one place left:
$ 37.4 \rightarrow 3.74 $

✔ Answer: $ 3.74 $

#### (b) $ 10.005 \div 10 $
- Move decimal one place left:
$ 10.005 \rightarrow 1.0005 $

✔ Answer: $ 1.0005 $

#### (c) $ 0.60 \div 10 $
- Move decimal one place left:
$ 0.60 \rightarrow 0.06 $

✔ Answer: $ 0.06 $

#### (d) $ 202.9 \div 10 $
- Move decimal one place left:
$ 202.9 \rightarrow 20.29 $

✔ Answer: $ 20.29 $

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2. Divide the decimals by a whole number:

We divide normally, keeping track of the decimal point.

#### (a) $ 3.9 \div 13 $
- Convert to fraction: $ \frac{3.9}{13} $
- Multiply numerator and denominator by 10 to eliminate decimal:
$ \frac{39}{130} $
- Simplify: $ \frac{39 \div 13}{130 \div 13} = \frac{3}{10} = 0.3 $

✔ Answer: $ 0.3 $

Alternatively, do long division:
```
0.3
------
13|3.9
-3.9
-----
0
```

✔ Answer: $ 0.3 $

#### (b) $ 0.056 \div 7 $
- Think: $ 56 \div 7 = 8 $, but since 0.056 has 3 decimal places, result is $ 0.008 $

Or:
- $ 0.056 \div 7 = ? $
- $ 56 \div 7 = 8 $, so $ 0.056 \div 7 = 0.008 $

✔ Answer: $ 0.008 $

#### (c) $ 3.024 \div 12 $
- Long division:
- $ 12 \div 3.024 $
- First, $ 12 \times 0.25 = 3.00 $, remainder $ 0.024 $
- $ 0.024 \div 12 = 0.002 $
- So total: $ 0.25 + 0.002 = 0.252 $

Check:
- $ 12 \times 0.252 = 3.024 $

✔ Answer: $ 0.252 $

#### (d) $ 0.288 \div 36 $
- Convert: $ \frac{0.288}{36} $
- Multiply numerator and denominator by 1000: $ \frac{288}{36000} $
- Simplify: $ \frac{288 \div 144}{36000 \div 144} = \frac{2}{250} = 0.008 $

Or:
- $ 288 \div 36 = 8 $, but since 0.288 has 3 decimal places, answer is $ 0.008 $

✔ Answer: $ 0.008 $

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3. Fill in the blanks:

#### (a) $ 0.005 \div 10 = $ ________
- Move decimal one place left: $ 0.005 \rightarrow 0.0005 $

✔ Answer: $ 0.0005 $

#### (b) $ 3712.8 \div 12 = $ ________
- Let's divide:
- $ 12 \times 300 = 3600 $
- Subtract: $ 3712.8 - 3600 = 112.8 $
- $ 12 \times 9 = 108 $ → $ 112.8 - 108 = 4.8 $
- $ 12 \times 0.4 = 4.8 $
- So total: $ 300 + 9 + 0.4 = 309.4 $

✔ Answer: $ 309.4 $

#### (c) $ 3.107 \div 10 = $ ________
- Move decimal one place left: $ 3.107 \rightarrow 0.3107 $

✔ Answer: $ 0.3107 $

#### (d) $ 27.3 \div 13 = $ ________
- $ 13 \times 2 = 26 $, remainder $ 1.3 $
- $ 1.3 \div 13 = 0.1 $
- So $ 2 + 0.1 = 2.1 $

Check: $ 13 \times 2.1 = 27.3 $

✔ Answer: $ 2.1 $

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✔ Final Answers:

#### 1.
(a) $ 3.74 $
(b) $ 1.0005 $
(c) $ 0.06 $
(d) $ 20.29 $

#### 2.
(a) $ 0.3 $
(b) $ 0.008 $
(c) $ 0.252 $
(d) $ 0.008 $

#### 3.
(a) $ 0.0005 $
(b) $ 309.4 $
(c) $ 0.3107 $
(d) $ 2.1 $

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