R3
Last Digit Cycle
末位数字循环
Remainder / 余数与循环Grades G5 - G8
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What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Very large exponent
- 2Question asks for the last digit
- 3Power of a specific number
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What It Really Tests
The core mathematical idea behind this structure:
The last digit of powers follows a short repeating cycle.
幂的末位数字遵循一个短循环。
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Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Trying to compute the entire large number
- ⚠Not noticing the cycle length
- ⚠Starting the cycle at the wrong point
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Your First Step
How to begin thinking about problems with this structure:
Write out the first 4-6 powers and look for where the last digit repeats.
写出前 4-6 个幂, 观察末位数字何时开始重复。
Related Structures
These structures share similar patterns or thinking approaches: