Express \(413_7\) to base 5
MATHEMATICS
WAEC 2023
Express \(413_7\) to base 5
- A. \(2311_5\)
- B. \(1131_5\)
- C. \(1311_5\)
- D. \(2132_5\)
Correct Answer: C. \(1311_5\)
Explanation
\(413_7\) to base 5
convert first to base 10
\(417_7 = 4 × 7^2 + 1 × 7^1 + 3 × 7^0\)
= 4 × 49 + 1 × 7 + 3 × 1
= 196 + 7 + 3
= \(206_{10}\)
convert this result to base 5
| 5 | 206 |
| 5 | 41R1 |
| 5 | 8R1 |
| 5 | 1R3 |
| 0R1 |
\(∴ 413_7 = 1311_5\)
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