Decimals and fractions - Fraction and Decimal Worksheets for Year - Free Printable

To solve the problems in the image, we need to convert fractions to decimals and decimals to fractions. Let's go through each section step by step.

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Section 1: Write these fractions as decimals

#### Part 1
1. $\frac{7}{10}$
- To convert a fraction to a decimal, divide the numerator by the denominator.
- $ \frac{7}{10} = 7 \div 10 = 0.7 $
- Answer: $ 0.7 $

2. $0.2$
- This is already a decimal, so no conversion is needed.
- Answer: $ 0.2 $

3. $\frac{5}{10}$
- $ \frac{5}{10} = 5 \div 10 = 0.5 $
- Answer: $ 0.5 $

#### Part 2
4. $\frac{3}{100}$
- $ \frac{3}{100} = 3 \div 100 = 0.03 $
- Answer: $ 0.03 $

5. $0.41$
- This is already a decimal, so no conversion is needed.
- Answer: $ 0.41 $

6. $\frac{67}{100}$
- $ \frac{67}{100} = 67 \div 100 = 0.67 $
- Answer: $ 0.67 $

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Section 2: Write these fractions as decimals

#### Part 1
1. $\frac{1}{10}$
- $ \frac{1}{10} = 1 \div 10 = 0.1 $
- Answer: $ 0.1 $

2. $\frac{1}{100}$
- $ \frac{1}{100} = 1 \div 100 = 0.01 $
- Answer: $ 0.01 $

3. $\frac{1}{1000}$
- $ \frac{1}{1000} = 1 \div 1000 = 0.001 $
- Answer: $ 0.001 $

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Section 3: Write these decimals as fractions

#### Part 1
1. $2.1$
- $ 2.1 = 2 + 0.1 $
- $ 0.1 = \frac{1}{10} $
- Therefore, $ 2.1 = 2 + \frac{1}{10} = \frac{20}{10} + \frac{1}{10} = \frac{21}{10} $
- Answer: $ \frac{21}{10} $

2. $0.8$
- $ 0.8 = \frac{8}{10} $
- Simplify $ \frac{8}{10} $ by dividing both numerator and denominator by 2:
$ \frac{8 \div 2}{10 \div 2} = \frac{4}{5} $
- Answer: $ \frac{4}{5} $

3. $0.5$
- $ 0.5 = \frac{5}{10} $
- Simplify $ \frac{5}{10} $ by dividing both numerator and denominator by 5:
$ \frac{5 \div 5}{10 \div 5} = \frac{1}{2} $
- Answer: $ \frac{1}{2} $

4. $0.3$
- $ 0.3 = \frac{3}{10} $
- Answer: $ \frac{3}{10} $

5. $0.6$
- $ 0.6 = \frac{6}{10} $
- Simplify $ \frac{6}{10} $ by dividing both numerator and denominator by 2:
$ \frac{6 \div 2}{10 \div 2} = \frac{3}{5} $
- Answer: $ \frac{3}{5} $

6. $0.9$
- $ 0.9 = \frac{9}{10} $
- Answer: $ \frac{9}{10} $

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Section 4: Change these decimals to fractions

#### Part 1
1. $0.50$
- $ 0.50 = \frac{50}{100} $
- Simplify $ \frac{50}{100} $ by dividing both numerator and denominator by 50:
$ \frac{50 \div 50}{100 \div 50} = \frac{1}{2} $
- Answer: $ \frac{1}{2} $

2. $0.25$
- $ 0.25 = \frac{25}{100} $
- Simplify $ \frac{25}{100} $ by dividing both numerator and denominator by 25:
$ \frac{25 \div 25}{100 \div 25} = \frac{1}{4} $
- Answer: $ \frac{1}{4} $

3. $0.75$
- $ 0.75 = \frac{75}{100} $
- Simplify $ \frac{75}{100} $ by dividing both numerator and denominator by 25:
$ \frac{75 \div 25}{100 \div 25} = \frac{3}{4} $
- Answer: $ \frac{3}{4} $

4. $0.20$
- $ 0.20 = \frac{20}{100} $
- Simplify $ \frac{20}{100} $ by dividing both numerator and denominator by 20:
$ \frac{20 \div 20}{100 \div 20} = \frac{1}{5} $
- Answer: $ \frac{1}{5} $

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Section 5: Change these decimals to fractions

#### Part 1
1. $0.39$
- $ 0.39 = \frac{39}{100} $
- Answer: $ \frac{39}{100} $

2. $0.47$
- $ 0.47 = \frac{47}{100} $
- Answer: $ \frac{47}{100} $

3. $0.21$
- $ 0.21 = \frac{21}{100} $
- Answer: $ \frac{21}{100} $

4. $0.83$
- $ 0.83 = \frac{83}{100} $
- Answer: $ \frac{83}{100} $

5. $0.91$
- $ 0.91 = \frac{91}{100} $
- Answer: $ \frac{91}{100} $

6. $0.51$
- $ 0.51 = \frac{51}{100} $
- Answer: $ \frac{51}{100} $

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Final Answer

$$
\boxed{
\begin{array}{ll}
\text{Section 1:} & 0.7, 0.2, 0.5, 0.03, 0.41, 0.67 \\
\text{Section 2:} & 0.1, 0.01, 0.001 \\
\text{Section 3:} & \frac{21}{10}, \frac{4}{5}, \frac{1}{2}, \frac{3}{10}, \frac{3}{5}, \frac{9}{10} \\
\text{Section 4:} & \frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{1}{5} \\
\text{Section 5:} & \frac{39}{100}, \frac{47}{100}, \frac{21}{100}, \frac{83}{100}, \frac{91}{100}, \frac{51}{100}
\end{array}
}
$$