Вычислите: (0,(6) − 0,(45)) · 0,(33)

  1. 0,(7)
  2. 0,(3)
  3. 0,(07)
  4. 0,(007)

📝 Detailed explanation

Переведем периодические дроби в обыкновенные: 0,(6) = ⁶/₉ = ²/₃; 0,(45) = ⁴⁵/₉₉ = ⁵/₁₁; 0,(33) = ³³/₉₉ = ¹/₃. В скобках: ²/₃ − ⁵/₁₁ = ²²/₃₃ − ¹⁵/₃₃ = ⁷/₃₃. Выполним умножение: ⁷/₃₃ · ¹/₃ = ⁷/₉₉ = 0,(07).
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