The value of \(0.5\bar 6 - 0.7\overline {23} + 0.3\bar 9 \times 0.\bar 7\) is:
Step 1 — Convert each recurring decimal to a fraction:
\(0.5\bar 6=\tfrac{56-5}{90}=\tfrac{51}{90}=\tfrac{17}{30}\); \(0.7\overline{23}=\tfrac{723-7}{990}=\tfrac{716}{990}\); \(0.3\bar 9=0.4=\tfrac{2}{5}\); \(0.\bar 7=\tfrac{7}{9}\).
Step 2 — Multiply first (BODMAS): \(\tfrac{2}{5}\times\tfrac{7}{9}=\tfrac{14}{45}\).
Step 3 — Combine over LCM 990:
\[\tfrac{17}{30}-\tfrac{716}{990}+\tfrac{14}{45}=\tfrac{561-716+308}{990}=\tfrac{153}{990}=\tfrac{17}{110}\]
Step 4 — Convert back: \(\tfrac{17}{110}=0.15454\ldots=0.1\overline{54}\).
Therefore the value is \(0.1\overline{54}\).
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Important Questions from Decimals
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If 19 × 23 = 437, then find the value of (190 × 0.023).
