📘 Question
Express the following rational numbers as decimals:
- (i) \( \frac{2}{3} \)
- (ii) \( -\frac{4}{9} \)
- (iii) \( -\frac{2}{15} \)
- (iv) \( -\frac{22}{13} \)
- (v) \( \frac{437}{999} \)
✏️ Step-by-Step Solution
(i) \( \frac{2}{3} \)
\[ \frac{2}{3} = 0.\overline{6} \] —(ii) \( -\frac{4}{9} \)
\[ -\frac{4}{9} = -0.\overline{4} \] —(iii) \( -\frac{2}{15} \)
\[ -\frac{2}{15} = -0.1333\ldots = -0.1\overline{3} \] —(iv) \( -\frac{22}{13} \)
\[ -\frac{22}{13} = -1.692307\overline{692307} \] —(v) \( \frac{437}{999} \)
\[ \frac{437}{999} = 0.\overline{437} \] —✅ Final Answers
- (i) \(0.\overline{6}\)
- (ii) \(-0.\overline{4}\)
- (iii) \(-0.1\overline{3}\)
- (iv) \(-1.\overline{692307}\)
- (v) \(0.\overline{437}\)
💡 Key Concept
- Denominator with factors other than 2,5 → recurring decimal
- \(\frac{n}{9} = 0.\overline{n}\)
- \(\frac{n}{999} = 0.\overline{n}\)