Question

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​

Answer 1

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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Answer 2

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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