Convert following to Rational Fractions $$ \begin{array}{l} ext { 1. } 1,30 \ 2.8, \dot{2} 3 \ 3 \cdot 0, \dot{2} \ 4 \cdot 1, \dot{3} \ 5 \cdot 7,82 \ ext { 6. 1,2 }\end{array} $$

Question

Convert following to Rational Fractions $$ \begin{array}{l}	ext { 1. } 1,30 \ 2.8, \dot{2} 3 \ 3 \cdot 0, \dot{2} \ 4 \cdot 1, \dot{3} \ 5 \cdot 7,82 \ 	ext { 6. 1,2 }\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's convert each of the given decimal numbers into rational fractions.

### 1. $$1,30$$
Interpreting the comma as a decimal point:
$$
1,30 = 1.30 = \frac{130}{100} = \frac{13}{10}
$$

### 2. $$8,\dot{2}3$$
Assuming the notation $$8,\dot{2}3$$ represents $$8.\overline{23}$$ (i.e., 8.232323...):
$$
x = 8.\overline{23}
$$
Multiply by 100 to shift the repeating part:
$$
100x = 823.\overline{23}
$$
Subtract the original equation:
$$
100x - x = 823.\overline{23} - 8.\overline{23} \
99x = 815 \
x = \frac{815}{99}
$$

### 3. $$0,\dot{2}$$
This represents $$0.\overline{2}$$ (i.e., 0.2222...):
$$
x = 0.\overline{2}
$$
Multiply by 10:
$$
10x = 2.\overline{2}
$$
Subtract the original equation:
$$
10x - x = 2.\overline{2} - 0.\overline{2} \
9x = 2 \
x = \frac{2}{9}
$$

### 4. $$1,\dot{3}$$
This represents $$1.\overline{3}$$ (i.e., 1.3333...):
$$
x = 1.\overline{3}
$$
Multiply by 10:
$$
10x = 13.\overline{3}
$$
Subtract the original equation:
$$
10x - x = 13.\overline{3} - 1.\overline{3} \
9x = 12 \
x = \frac{12}{9} = \frac{4}{3}
$$

### 5. $$7,82$$
Interpreting the comma as a decimal point:
$$
7,82 = 7.82 = \frac{782}{100} = \frac{391}{50}
$$

### 6. $$1,2$$
Interpreting the comma as a decimal point:
$$
1,2 = 1.2 = \frac{12}{10} = \frac{6}{5}
$$

### **Summary of Rational Fractions**
1. $$1,30 = \frac{13}{10}$$
2. $$8,\dot{2}3 = \frac{815}{99}$$
3. $$0,\dot{2} = \frac{2}{9}$$
4. $$1,\dot{3} = \frac{4}{3}$$
5. $$7,82 = \frac{391}{50}$$
6. $$1,2 = \frac{6}{5}$$
1. $$1,30 = \frac{13}{10}$$ 2. $$8,\dot{2}3 = \frac{815}{99}$$ 3. $$0,\dot{2} = \frac{2}{9}$$ 4. $$1,\dot{3} = \frac{4}{3}$$ 5. $$7,82 = \frac{391}{50}$$ 6. $$1,2 = \frac{6}{5}$$

Convert following to Rational Fractions

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Summary of Rational Fractions

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