\(\frac{0.1667 \times 0.8333 \times 0.3333}{0.2222 \times 0.6667 \times 0.1250}\) is approximately equal to:
2.5
Each decimal here is the recurring form of a simple fraction, so replace them to make the arithmetic exact.
In the numerator, \(0.1667\approx\tfrac{1}{6}\), \(0.8333\approx\tfrac{5}{6}\), and \(0.3333\approx\tfrac{1}{3}\).
In the denominator, \(0.2222\approx\tfrac{2}{9}\), \(0.6667\approx\tfrac{2}{3}\), and \(0.1250 = \tfrac{1}{8}\) exactly.
Numerator = \(\tfrac{1}{6}\times\tfrac{5}{6}\times\tfrac{1}{3} = \tfrac{5}{108}\).
Denominator = \(\tfrac{2}{9}\times\tfrac{2}{3}\times\tfrac{1}{8} = \tfrac{4}{216} = \tfrac{1}{54}\).
Divide: \(\tfrac{5}{108} \div \tfrac{1}{54} = \tfrac{5}{108}\times 54 = \tfrac{5}{2} = 2.5\).
The key idea is recognising each repeating decimal as its fraction, which turns a messy product into a clean cancellation. The value is approximately 2.5.
Similar Questions
\(\frac{0.1667 \times 0.8333 \times 0.3333}{0.2222 \times 0.6667 \times 0.1250}\) is approximately equal to:
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