Free Printable Converting Decimals to Fractions Worksheets - Free Printable

Problem Overview:

The task is to convert decimals into fractions, following specific rules:
1. The denominator of the fraction should be a power of 10 (e.g., 10, 100, 1000).
2. If the decimal is greater than 1, express it as a mixed fraction.
3. Do not simplify the fractions.

Solution Explanation:

#### Step 1: Understanding the Conversion Process
- Decimals to Fractions:
- A decimal can be directly converted to a fraction by placing the decimal number over a denominator that is a power of 10. The number of decimal places determines the power of 10.
- For example:
- \(0.6\) has one decimal place, so it becomes \(\frac{6}{10}\).
- \(0.34\) has two decimal places, so it becomes \(\frac{34}{100}\).
- \(0.325\) has three decimal places, so it becomes \(\frac{325}{1000}\).

- Mixed Fractions:
- If the decimal is greater than 1, separate the whole number part from the fractional part.
- For example:
- \(1.8\) becomes \(1 \frac{8}{10}\).
- \(3.4\) becomes \(3 \frac{4}{10}\).
- \(7.28\) becomes \(7 \frac{28}{100}\).

#### Step 2: Applying the Rules
Let's go through a few examples to illustrate the process:

1. Example 1: Convert \(0.6\) to a fraction
- \(0.6\) has one decimal place.
- Place \(6\) over \(10\): \(\frac{6}{10}\).

2. Example 2: Convert \(0.34\) to a fraction
- \(0.34\) has two decimal places.
- Place \(34\) over \(100\): \(\frac{34}{100}\).

3. Example 3: Convert \(1.8\) to a mixed fraction
- Separate the whole number part (\(1\)) and the decimal part (\(0.8\)).
- Convert \(0.8\) to a fraction: \(\frac{8}{10}\).
- Combine: \(1 \frac{8}{10}\).

4. Example 4: Convert \(3.4\) to a mixed fraction
- Separate the whole number part (\(3\)) and the decimal part (\(0.4\)).
- Convert \(0.4\) to a fraction: \(\frac{4}{10}\).
- Combine: \(3 \frac{4}{10}\).

5. Example 5: Convert \(0.325\) to a fraction
- \(0.325\) has three decimal places.
- Place \(325\) over \(1000\): \(\frac{325}{1000}\).

6. Example 6: Convert \(7.28\) to a mixed fraction
- Separate the whole number part (\(7\)) and the decimal part (\(0.28\)).
- Convert \(0.28\) to a fraction: \(\frac{28}{100}\).
- Combine: \(7 \frac{28}{100}\).

#### Step 3: Verifying the Provided Answers
The provided answers in the image are already filled in, and they follow the rules correctly. Here are a few verifications:

- \(0.6 = \frac{6}{10}\): Correct.
- \(0.34 = \frac{34}{100}\): Correct.
- \(1.8 = 1 \frac{8}{10}\): Correct.
- \(3.4 = 3 \frac{4}{10}\): Correct.
- \(0.325 = \frac{325}{1000}\): Correct.
- \(7.28 = 7 \frac{28}{100}\): Correct.

All the answers in the image are consistent with the rules provided.

Final Answer:

The solutions in the image are correct. Here is the confirmation:

\[
\boxed{\text{All answers are correct as per the rules.}}
\]