Fractions to Decimals - Free Math Worksheets - Free Printable

Let's solve the problem step by step.

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Task: Convert each fraction to its decimal form.

We are given a list of fractions with denominators of 10, 100, or 1000. These are decimal fractions, meaning they can be easily converted to decimals by placing the numerator in the correct decimal place based on the denominator.

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Rules for Conversion:

- If the denominator is 10, move the decimal point one place to the left.
- If the denominator is 100, move the decimal point two places to the left.
- If the denominator is 1000, move the decimal point three places to the left.

For example:
- $ \frac{7}{10} = 0.7 $
- $ \frac{15}{100} = 0.15 $
- $ \frac{112}{1000} = 0.112 $

Now let’s convert all the fractions:

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Solutions:

#### Column 1
1. $ \frac{7}{10} = 0.7 $ ✔ (already given)
2. $ \frac{8}{10} = 0.8 $
3. $ \frac{9}{10} = 0.9 $
4. $ \frac{7}{100} = 0.07 $
5. $ \frac{3}{100} = 0.03 $
6. $ \frac{46}{100} = 0.46 $
7. $ \frac{8}{100} = 0.08 $
8. $ \frac{247}{10} = 24.7 $
9. $ \frac{68}{100} = 0.68 $
10. $ \frac{27}{10} = 2.7 $

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#### Column 2
1. $ \frac{15}{100} = 0.15 $ ✔ (already given)
2. $ \frac{24}{100} = 0.24 $
3. $ \frac{58}{100} = 0.58 $
4. $ \frac{3}{1000} = 0.003 $
5. $ \frac{4}{1000} = 0.004 $
6. $ \frac{2}{1000} = 0.002 $
7. $ \frac{9}{1000} = 0.009 $
8. $ \frac{423}{100} = 4.23 $
9. $ \frac{302}{1000} = 0.302 $
10. $ \frac{603}{100} = 6.03 $

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#### Column 3
1. $ \frac{112}{1000} = 0.112 $
2. $ \frac{256}{1000} = 0.256 $
3. $ \frac{401}{1000} = 0.401 $
4. $ \frac{39}{1000} = 0.039 $
5. $ \frac{12}{1000} = 0.012 $
6. $ \frac{73}{1000} = 0.073 $
7. $ \frac{98}{1000} = 0.098 $
8. $ \frac{902}{1000} = 0.902 $
9. $ \frac{78}{1000} = 0.078 $
10. $ \frac{55}{1000} = 0.055 $

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#### Column 4
1. $ \frac{12}{1000} = 0.012 $
2. $ \frac{43}{1000} = 0.043 $
3. $ \frac{22}{1000} = 0.022 $
4. $ \frac{198}{1000} = 0.198 $
5. $ \frac{401}{1000} = 0.401 $
6. $ \frac{28}{100} = 0.28 $
7. $ \frac{35}{100} = 0.35 $
8. $ \frac{101}{10} = 10.1 $
9. $ \frac{2345}{100} = 23.45 $
10. $ \frac{78}{10} = 7.8 $

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✔ Final Answer List (in order):

| Fraction | Decimal |
|--------|--------|
| $ \frac{7}{10} $ | 0.7 |
| $ \frac{8}{10} $ | 0.8 |
| $ \frac{9}{10} $ | 0.9 |
| $ \frac{7}{100} $ | 0.07 |
| $ \frac{3}{100} $ | 0.03 |
| $ \frac{46}{100} $ | 0.46 |
| $ \frac{8}{100} $ | 0.08 |
| $ \frac{247}{10} $ | 24.7 |
| $ \frac{68}{100} $ | 0.68 |
| $ \frac{27}{10} $ | 2.7 |
| $ \frac{15}{100} $ | 0.15 |
| $ \frac{24}{100} $ | 0.24 |
| $ \frac{58}{100} $ | 0.58 |
| $ \frac{3}{1000} $ | 0.003 |
| $ \frac{4}{1000} $ | 0.004 |
| $ \frac{2}{1000} $ | 0.002 |
| $ \frac{9}{1000} $ | 0.009 |
| $ \frac{423}{100} $ | 4.23 |
| $ \frac{302}{1000} $ | 0.302 |
| $ \frac{603}{100} $ | 6.03 |
| $ \frac{112}{1000} $ | 0.112 |
| $ \frac{256}{1000} $ | 0.256 |
| $ \frac{401}{1000} $ | 0.401 |
| $ \frac{39}{1000} $ | 0.039 |
| $ \frac{12}{1000} $ | 0.012 |
| $ \frac{73}{1000} $ | 0.073 |
| $ \frac{98}{1000} $ | 0.098 |
| $ \frac{902}{1000} $ | 0.902 |
| $ \frac{78}{1000} $ | 0.078 |
| $ \frac{55}{1000} $ | 0.055 |
| $ \frac{12}{1000} $ | 0.012 |
| $ \frac{43}{1000} $ | 0.043 |
| $ \frac{22}{1000} $ | 0.022 |
| $ \frac{198}{1000} $ | 0.198 |
| $ \frac{401}{1000} $ | 0.401 |
| $ \frac{28}{100} $ | 0.28 |
| $ \frac{35}{100} $ | 0.35 |
| $ \frac{101}{10} $ | 10.1 |
| $ \frac{2345}{100} $ | 23.45 |
| $ \frac{78}{10} $ | 7.8 |

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✔ Summary of Key Concepts:

- The number of zeros in the denominator tells you how many decimal places to use.
- For $ \frac{a}{10} $ → one decimal place
- For $ \frac{a}{100} $ → two decimal places
- For $ \frac{a}{1000} $ → three decimal places

This method works perfectly because these are powers of 10, making conversion straightforward.

Let me know if you'd like this as a printable answer key!