GuruXpert Academy
O-Level Mathematics
ZIMSEC • Cambridge • GCSE • Other Syllabuses
ZIMSEC • Cambridge • GCSE • Other Syllabuses
NUMBER BASES
O-LEVEL QUESTION
Express 1 × 34 + 32 + 2 as a number in base 3 [1].
Solution
Original number:
1 × 34
+ 32
+ 2
First, write all the powers of 3 in descending order: 4, 3, 2, 1, 0 .
Now identify the coefficient of each power. A power that is missing has a coefficient of 0.
Coefficients of the powers:
34
→ coefficient =
1
33
→ coefficient =
0
32
→ coefficient =
1
31
→ coefficient =
0
30
→ coefficient =
2
Therefore, the coefficients in the order 34, 33, 32, 31, 30 are:
1, 0, 1, 0, 2
=
1 × 34
+ 0 × 33
+ 1 × 32
+ 0 × 31
+ 2 × 30
FINAL CONVERSION TO BASE 3
1 0 1 0 23
Answer:
101023
Quick Verification
=
101023
=
1(81) + 0(27) + 1(9) + 0(3) + 2(1)
=
9210
✓ Matches the original value.
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