what can be the easiest method of knowing the unit digits of bigger exponents?
what can be the easiest method of knowing the unit digits of bigger exponents?
saurav sahoo , 10 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> what can be the easiest method of knowing...
1 AnswersArnav Prasad
Every number from 0 ---> 9 has a definite cycle of repetition of unit’s digit.
For example, take 3.
31 = 3. Unit’s digit is 3.
32 = 9. Unit’s digit is 9.
33 = 27. Unit’s digit is 7.
34 = 81. Unit’s digit is 1.
And then again, 35 = 243. Unit’s digit is 3.
The cycle repeated after every 4 exponents.
If you want to take out unit’s digit of 931025, OR 1257831025 or anything ending with 31025.
Just focus at the unit’s digit, as if, it is written 31025.
You know the unit’s cycle repeats after every 4 exponents.
Divide 1025 by 4. Remainder is 1.
Unit’s place of 31025 is EXACTLY same as unit’s place of 31.
Thus, unit’s place of 931025 or 1257831025 is 3.
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