Converting Decimals to Fractions Worksheet - Free Printable

To solve the problem of converting decimals into decimal fractions and then simplifying them to their simplest form, we will follow these steps:

Steps:

1. Convert the Decimal to a Fraction:
- Write the decimal as a fraction with the decimal number as the numerator and the place value of the last digit as the denominator.
- For example, for \(0.34\), the last digit is in the hundredths place, so the fraction is \(\frac{34}{100}\).

2. Simplify the Fraction:
- Find the greatest common divisor (GCD) of the numerator and the denominator.
- Divide both the numerator and the denominator by their GCD to get the fraction in its simplest form.
- For example, for \(\frac{34}{100}\), the GCD of 34 and 100 is 2, so \(\frac{34 \div 2}{100 \div 2} = \frac{17}{50}\).

Now, let's solve each problem step by step.

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1. \(0.34\)

- Decimal fraction: \(\frac{34}{100}\)
- Simplest form: \(\frac{34 \div 2}{100 \div 2} = \frac{17}{50}\)

2. \(0.05\)

- Decimal fraction: \(\frac{5}{100}\)
- Simplest form: \(\frac{5 \div 5}{100 \div 5} = \frac{1}{20}\)

3. \(0.14\)

- Decimal fraction: \(\frac{14}{100}\)
- Simplest form: \(\frac{14 \div 2}{100 \div 2} = \frac{7}{50}\)

4. \(0.125\)

- Decimal fraction: \(\frac{125}{1000}\)
- Simplest form: \(\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}\)

5. \(0.64\)

- Decimal fraction: \(\frac{64}{100}\)
- Simplest form: \(\frac{64 \div 4}{100 \div 4} = \frac{16}{25}\)

6. \(0.27\)

- Decimal fraction: \(\frac{27}{100}\)
- Simplest form: \(\frac{27}{100}\) (already in simplest form)

7. \(0.216\)

- Decimal fraction: \(\frac{216}{1000}\)
- Simplest form: \(\frac{216 \div 8}{1000 \div 8} = \frac{27}{125}\)

8. \(0.89\)

- Decimal fraction: \(\frac{89}{100}\)
- Simplest form: \(\frac{89}{100}\) (already in simplest form)

9. \(0.625\)

- Decimal fraction: \(\frac{625}{1000}\)
- Simplest form: \(\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}\)

10. \(0.428\)

- Decimal fraction: \(\frac{428}{1000}\)
- Simplest form: \(\frac{428 \div 4}{1000 \div 4} = \frac{107}{250}\)

11. \(0.08\)

- Decimal fraction: \(\frac{8}{100}\)
- Simplest form: \(\frac{8 \div 4}{100 \div 4} = \frac{2}{25}\)

12. \(0.546\)

- Decimal fraction: \(\frac{546}{1000}\)
- Simplest form: \(\frac{546 \div 2}{1000 \div 2} = \frac{273}{500}\)

13. \(0.35\)

- Decimal fraction: \(\frac{35}{100}\)
- Simplest form: \(\frac{35 \div 5}{100 \div 5} = \frac{7}{20}\)

14. \(0.864\)

- Decimal fraction: \(\frac{864}{1000}\)
- Simplest form: \(\frac{864 \div 8}{1000 \div 8} = \frac{108}{125}\)

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Final Answer:

\[
\boxed{
\begin{array}{ccc}
\text{Decimal} & \text{Decimal fraction} & \text{Simplest form} \\
0.05 & \frac{5}{100} & \frac{1}{20} \\
0.14 & \frac{14}{100} & \frac{7}{50} \\
0.125 & \frac{125}{1000} & \frac{1}{8} \\
0.64 & \frac{64}{100} & \frac{16}{25} \\
0.27 & \frac{27}{100} & \frac{27}{100} \\
0.216 & \frac{216}{1000} & \frac{27}{125} \\
0.89 & \frac{89}{100} & \frac{89}{100} \\
0.625 & \frac{625}{1000} & \frac{5}{8} \\
0.428 & \frac{428}{1000} & \frac{107}{250} \\
0.08 & \frac{8}{100} & \frac{2}{25} \\
0.546 & \frac{546}{1000} & \frac{273}{500} \\
0.35 & \frac{35}{100} & \frac{7}{20} \\
0.864 & \frac{864}{1000} & \frac{108}{125} \\
\end{array}
}
\]