Converting Decimals to Fractions Worksheet - 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. Do not simplify the fractions.
3. If the decimal is greater than one, express it as a mixed fraction.

Solution Explanation:

#### Step 1: Understanding the Conversion Process
- Decimals to Fractions: To convert a decimal to a fraction, place the decimal number over a denominator that is a power of 10 based on the number of decimal places.
- For example:
- \(0.6\) has one decimal place, so the fraction is \(\frac{6}{10}\).
- \(0.34\) has two decimal places, so the fraction is \(\frac{34}{100}\).
- \(0.325\) has three decimal places, so the fraction is \(\frac{325}{1000}\).

- Mixed Fractions for Decimals Greater Than One: If the decimal is greater than one, separate the whole number part from the fractional part.
- For example:
- \(1.8 = 1 + 0.8\), so the mixed fraction is \(1 \frac{8}{10}\).
- \(3.4 = 3 + 0.4\), so the mixed fraction is \(3 \frac{4}{10}\).

#### Step 2: Applying the Rules to Each Decimal
We will go through each decimal and convert it to a fraction or mixed fraction as required.

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Detailed Solutions:

#### Part 1: Decimals Less Than One
1. \(0.6 = \frac{6}{10}\)
2. \(0.3 = \frac{3}{10}\)
3. \(0.1 = \frac{1}{10}\)
4. \(0.9 = \frac{9}{10}\)
5. \(0.8 = \frac{8}{10}\)
6. \(0.27 = \frac{27}{100}\)
7. \(0.58 = \frac{58}{100}\)
8. \(0.81 = \frac{81}{100}\)
9. \(0.43 = \frac{43}{100}\)
10. \(0.92 = \frac{92}{100}\)
11. \(0.78 = \frac{78}{100}\)
12. \(0.55 = \frac{55}{100}\)
13. \(0.34 = \frac{34}{100}\)
14. \(0.2 = \frac{2}{10}\)
15. \(0.81 = \frac{81}{100}\)
16. \(0.7 = \frac{7}{10}\)
17. \(0.325 = \frac{325}{1000}\)
18. \(0.289 = \frac{289}{1000}\)
19. \(0.452 = \frac{452}{1000}\)
20. \(0.013 = \frac{13}{1000}\)
21. \(0.67 = \frac{67}{100}\)
22. \(0.29 = \frac{29}{100}\)
23. \(0.316 = \frac{316}{1000}\)
24. \(0.527 = \frac{527}{1000}\)

#### Part 2: Decimals Greater Than One
25. \(1.8 = 1 \frac{8}{10}\)
26. \(3.4 = 3 \frac{4}{10}\)
27. \(2.63 = 2 \frac{63}{100}\)
28. \(9.6 = 9 \frac{6}{10}\)
29. \(4.39 = 4 \frac{39}{100}\)
30. \(7.28 = 7 \frac{28}{100}\)
31. \(0.375 = \frac{375}{1000}\) (This is less than one, so no mixed fraction needed.)
32. \(6.41 = 6 \frac{41}{100}\)
33. \(1.372 = 1 \frac{372}{1000}\)
34. \(5.391 = 5 \frac{391}{1000}\)
35. \(8.29 = 8 \frac{29}{100}\)
36. \(11.83 = 11 \frac{83}{100}\)

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Final Answer:

The completed worksheet with all answers is as follows:

\[
\boxed{
\begin{array}{lll}
1) & 0.6 = \frac{6}{10} & 13) & 0.34 = \frac{34}{100} & 25) & 1.8 = 1 \frac{8}{10} \\
2) & 0.3 = \frac{3}{10} & 14) & 0.2 = \frac{2}{10} & 26) & 3.4 = 3 \frac{4}{10} \\
3) & 0.1 = \frac{1}{10} & 15) & 0.81 = \frac{81}{100} & 27) & 2.63 = 2 \frac{63}{100} \\
4) & 0.9 = \frac{9}{10} & 16) & 0.7 = \frac{7}{10} & 28) & 9.6 = 9 \frac{6}{10} \\
5) & 0.8 = \frac{8}{10} & 17) & 0.325 = \frac{325}{1000} & 29) & 4.39 = 4 \frac{39}{100} \\
6) & 0.27 = \frac{27}{100} & 18) & 0.289 = \frac{289}{1000} & 30) & 7.28 = 7 \frac{28}{100} \\
7) & 0.58 = \frac{58}{100} & 19) & 0.452 = \frac{452}{1000} & 31) & 0.375 = \frac{375}{1000} \\
8) & 0.81 = \frac{81}{100} & 20) & 0.013 = \frac{13}{1000} & 32) & 6.41 = 6 \frac{41}{100} \\
9) & 0.43 = \frac{43}{100} & 21) & 0.67 = \frac{67}{100} & 33) & 1.372 = 1 \frac{372}{1000} \\
10) & 0.92 = \frac{92}{100} & 22) & 0.29 = \frac{29}{100} & 34) & 5.391 = 5 \frac{391}{1000} \\
11) & 0.78 = \frac{78}{100} & 23) & 0.316 = \frac{316}{1000} & 35) & 8.29 = 8 \frac{29}{100} \\
12) & 0.55 = \frac{55}{100} & 24) & 0.527 = \frac{527}{1000} & 36) & 11.83 = 11 \frac{83}{100} \\
\end{array}
}
\]