If 40% of 10% of \(\dfrac{1}{3}\) of a number is 477, find the number.
35775
Let the number be \(N\). The condition gives \(\dfrac{40}{100} \times \dfrac{10}{100} \times \dfrac{1}{3} \times N = 477\).
Simplify the coefficient: \(\dfrac{2}{5} \times \dfrac{1}{10} \times \dfrac{1}{3} = \dfrac{2}{150} = \dfrac{1}{75}\).
So \(\dfrac{N}{75} = 477\).
\(N = 477 \times 75 = 35775\).
Hence, the number is 35775.
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