Maths Olympiad Prep

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Number theory Difficulty 5.5 AIME, harder Find the answer

Example 7(736)87(736)_{8} converted to a decimal number equals what?

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.

Solution

Solve (736)8=7×82+3×8+6=448+24+6=478.\begin{aligned}(736)_{8} & =7 \times 8^{2}+3 \times 8+6=448+24 \\ & +6=478 .\end{aligned}

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.