Find the units place of the number
34989843? (Number system 1)
Select one:
O a. 8
O b. 4
O c. 2
O d. 6
Answers
Given :- Find the units place of the number 34^989843 ? (Number system 1)
Select one:
O a. 8
O b. 4
O c. 2
O d. 6
Solution :-
we know that,
- 4¹ = 4 => unit digit 4 .
- 4² = 16 => unit digit 6 .
- 4³ = 64 => unit digit 4 .
- 4⁴ = 256 => unit digit 6 .
- unit digit will repeat after that, or (4⁵ = 4⁴ * 4)
so, we can conclude that, unit digit of 4 will be either 4 or 6 .
then,
→ (34)^989843
→ (34)^(247460 * 4 + 3)
checking unit digit of 34 as 4 only ,
→ (4)^(247460 * 4) * (4)³
now since power (247460 * 4) is divisible by 4, unit digit will be 4⁴ = 6 .
then,
→ 6 * (64 unit digit 4)
→ 6 * 4
→ 24 = unit digit 4 (B) (Ans.)
[ Remember :- we have to divide the power by 4, if remainder is 1, unit digit will be 4¹ unit digit, if remainder is 2, unit digit will be 4¹ unit digit , if remainder is 3, unit digit will be 4³ unit digit and if remainder is 0, unit digit will be 4⁴ unit digit . We can use this concept in all finding unit digit questions. ]
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Given : (349898)⁴³ or ( 3498)⁹⁸⁴³
To Find : Unit Place
O a. 8
O b. 4
O c. 2
O d. 6
Solution:
Note : Why (349898)⁴⁰ * (349898)³ is considered
as 8 raised to power to different numbers can lead to any of the given options ( 2 , 4 , 6 or 8)
power to ending with 3 or 9 will lead in odd numbers
and power to ending with 4 will lead in ending with 4 or 6 only.
8¹ = 8 Ends with 8
8² = 64 Ends with 4
8³ = 512 Ends with 2
8⁴ = 4096 Ends with 6
6ⁿ ends with n n ≥ 1
(349898)⁴³
= (349898)⁴⁰ * (349898)³
= (349898⁴)¹⁰ * (349898)³
= ends with 6 * ( Ends with 2)
= 6 * 2 = 12
Hence ends with 2
( 3498)⁹⁸⁴³
= = (3498)⁹⁸⁴⁰ * (3498)³
= (349898⁴)²⁴⁶⁰* (349898)³
= (Ends with 6) * ( Ends with 2)
= 6 * 2 = 12
Hence ends with 2
(349898)⁴³ or ( 3498)⁹⁸⁴³
Both Ends with 2
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