# Lösungen: Dezimalzahlen und Brüche (Basis)

A. Rechne die folgenden Zahlen in Dezimalbrüche (Zehnerbrüche) um und kürze anschließend, falls möglich.

1. $$0,2 = \bbox[#e1ffc1,5px]{ \frac{2}{10} = \frac{1}{5} }$$

2. $$0,5 = \bbox[#e1ffc1,5px]{ \frac{5}{10} = \frac{1}{2} }$$

3. $$1,5 = \bbox[#e1ffc1,5px]{ \frac{15}{10} = \frac{3}{2} }$$

4. $$0,125 = \bbox[#e1ffc1,5px]{ \frac{125}{1000} = \frac{1}{8} }$$

5. $$0,05 = \bbox[#e1ffc1,5px]{ \frac{5}{100} = \frac{1}{20} }$$

6. $$0,45 = \bbox[#e1ffc1,5px]{ \frac{45}{100} = \frac{9}{20} }$$

7. $$0,25 = \bbox[#e1ffc1,5px]{ \frac{25}{100} = \frac{1}{4} }$$

8. $$2,25 = \bbox[#e1ffc1,5px]{ \frac{225}{100} = \frac{9}{4} }$$

9. $$5,5 = \bbox[#e1ffc1,5px]{ \frac{55}{10} = \frac{11}{2} }$$

10. $$3,1 = \bbox[#e1ffc1,5px]{ \frac{31}{10} = \frac{31}{10} }$$

11. $$4,15 = \bbox[#e1ffc1,5px]{ \frac{415}{100} = \frac{83}{20} }$$

12. $$10,75 = \bbox[#e1ffc1,5px]{ \frac{1075}{100} = \frac{43}{4} }$$

B. Rechne die folgenden Brüche zuerst in Dezimalbrüche (Zehnerbrüche) um, sofern möglich, und danach in Kommazahlen. Falls nötig, runde auf fünf Nachkommastellen.

1. $$\frac{1}{2} = \bbox[#e1ffc1,5px]{ \frac{5}{10} = 0,5 }$$

2. $$\frac{1}{4} = \bbox[#e1ffc1,5px]{ \frac{25}{100} = 0,25 }$$

3. $$\frac{1}{5} = \bbox[#e1ffc1,5px]{ \frac{2}{10} = 0,2 }$$

4. $$\frac{1}{8} = \bbox[#e1ffc1,5px]{ \frac{125}{1000} = 0,125 }$$

5. $$\frac{1}{20} = \bbox[#e1ffc1,5px]{ \frac{5}{100} = 0,05 }$$

6. $$\frac{5}{100} = \bbox[#e1ffc1,5px]{ 0,05 }$$

7. $$\frac{20}{200} = \bbox[#e1ffc1,5px]{ \frac{1}{10} = 0,1 }$$

8. $$\frac{15}{1000} = \bbox[#e1ffc1,5px]{ 0,015 }$$

9. $$\frac{1}{3} \approx \bbox[#e1ffc1,5px]{ 0,33333 }$$

10. $$\frac{1}{6} \approx \bbox[#e1ffc1,5px]{ 0,16667 }$$

11. $$\frac{2}{13} \approx \bbox[#e1ffc1,5px]{ 0,15385 }$$

12. $$\frac{4}{15} \approx \bbox[#e1ffc1,5px]{ 0,26667 }$$

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