The integer in units place of 9^999 is

M4maths Previous Puzzles

08 Mar 2010 Unit place?

The integer in units place of 9^999 is

OPtion

1) 9
2) 8
3) 7
4) 6
5) 5
6) 4
7) 3
8) 2
9) 1
10) 0

Solution

999 is an odd number

		9*9 = 81 => a pair of 9 has 1 in units place 

		Thus 9999 = 81*81*81*81*81*81*81……………..*9

		The integer at units place is 9

Correct Option: 1 Best Solution (13)

Dr.Dipin Singh   14 years AGO

9^1=9 and ... 9^2=81...9^3 = 729 ....

In this way , we find that for 9^1,9^3,9^5, or 9 ^ ( any odd power) , the integer at unit place will be 9 .

......... Hence The integer in units place of 9^999 is 9... option 1

Like? Yes (1) | No   

Pargat Pal Singh   14 years AGO

9^1=9 and ; 9^2=81 ; 9^3 = 729 ....

So it is clear that for 9 ^ ( any odd power) , the integer at unit place will be 9 and for 9 ^ ( any even power) , the integer at unit place will be 1.

Now here 999 is an odd number.

The integer in units place of 9^999 will be 9.

Like? Yes (1) | No   

S. Singh   14 years AGO

9 ^ 999 , the integer at unit place will be 9 because for 9 ^ ( any odd power) , the integer at unit place will be 9 and for 9 ^ ( any even power) , the integer at unit place will be 1. check in
9^1=9, 9^3 =729, 9^5 = 59049 and so on ....

Like? Yes (1) | No   

Bawa   14 years AGO

For 9 ^ ( odd power) like 9^1,9^3,9^5 , the integer at unit place will be 9.

so for 9^999, the integer at unit place will be 9.

Like? Yes (1) | No   

Saranjit Singh   14 years AGO

9 ^ 999 , the integer at unit place will be 9 .
Observe that 9^1=9,9^2=81, 9^3 =729, 9^5 = 59049 and so on ....
Here for 9 ^ ( any odd power) , the integer at unit place will be 9 and for 9 ^ ( any even power) , the integer at unit place will be 1.

Like? Yes (1) | No   

Mayur   14 years AGO

9 ^ 999 , the integer at unit place will be 9 as for 9 ^ ( any odd power) , the integer at unit place is 9.

Like? Yes (1) | No   

Jagat   14 years AGO

9 ^ 999 , the integer at unit place will be 9 as for 9 ^ ( any odd power) , the integer at unit place will be 9 and for 9 ^ ( any even power) , the integer at unit place will be 1.

Like? Yes (1) | No   

Achelal Sharma   14 years AGO

the value for the odd power in the units place will be 9

Like? Yes (1) | No   

sivakumar   14 years AGO

if 9 to the power odd number the unit place integer will be 9 and 9 to the power even number the unit place integer will be 1. here 9^999, the answer is 9.

Like? Yes (1) | No   

rohit kumar   14 years AGO

even powers to 9 gives 1 as unit place and odd powers to 9 gives 9 only as unit place.

Like? Yes (1) | No   

sujit   14 years AGO

9^1=9
9^2=81
9^3=729
we see that for odd powers the unit place digit is 9
and for even power the unit place digit is 1.

Like? Yes (1) | No   

nitin sakhala   14 years AGO

as
9*9=81
9*9*9=729
9*9*9*9=6561
.
.
.
.
going this way we get 9 at unit's place of9^999(odd times multiplication)

Like? Yes (1) | No   

Siddharth Gupta   14 years AGO

[{(9)^4}^249] * (9)^3

Like? Yes (1) | No