Question 3 of 22intermediate🔧 ApplyNumerical5 marks

Write the following numbers in the above base-5 system using the symbols in Table 2: 15, 50, 137, 293, 651.

(i)
Answer

30 (base-5)

(ii)
Answer

200 (base-5)

(iii)
Answer

1022 (base-5)

(iv)
Answer

2133 (base-5)

(v)
Answer

10101 (base-5)

Explanation

(i) 15 = 3×53 \times 5 + 0×10 \times 1, so in base-5 it is 30. (ii) 50 = 2×252 \times 25 + 0×50 \times 5 + 0×10 \times 1, so in base-5 it is 200. (iii) 137 = 1×1251 \times 125 + 0×250 \times 25 + 2×52 \times 5 + 2×12 \times 1, so in base-5 it is 1022. (iv) 293 = 2×1252 \times 125 + 1×251 \times 25 + 3×53 \times 5 + 3×13 \times 1, so in base-5 it is 2133. (v) 651 = 1×6251 \times 625 + 0×1250 \times 125 + 1×251 \times 25 + 0×50 \times 5 + 1×11 \times 1, so in base-5 it is 10101.

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