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| Math Central | Quandaries & Queries |
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Question from Usama, a student: Convert the numbers used in the following expressions into those of base-five and solve : |
Hi Usama,
I can help get you started by converting 108 to base 5.
108 divided by 5 is 21 with a remainder of 3 so $108 = 21 \times 5 + 3.$ Next 21 divided by 5 is 4 with a remainder of 1. Hence
\[108 = 21 \times 5 + 3 = (4 \times 5 + 1) \times 5 + 3 = 4 \times 5^2 + 1 \times 5 + 3 = 413_5\]
Try to complete the problem now and write back if you need more assistance,
Penny
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