Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

what will be the unit digit of (3^2013)
Asked by Mohit kumar | 26 Mar, 2014, 07:31: AM
answered-by-expert Expert Answer
Let us consider the powers of 3
3 to the power of 1 equals 3 3 squared equals 9 3 cubed equals 27 3 to the power of 4 equals 81 3 to the power of 5 equals 243 3 to the power of 6 equals 729 . . . . .
 
Let us now consider only the unit digits of powers of 3.
 
T h u s comma space w e space h a v e 3 to the power of 1 space h a s space u n i t space d i g i t space 3 3 squared space h a s space u n i t space d i g i t space 9 3 cubed space h a s space u n i t space d i g i t space 7 3 to the power of 4 space h a s space u n i t space d i g i t space 1 3 to the power of 5 space h a s space u n i t space d i g i t space 3 3 to the power of 6 space h a s space u n i t space d i g i t space 9 3 to the power of 7 space h a s space u n i t space d i g i t space 7 3 to the power of 8 space h a s space u n i t space d i g i t space 1 3 to the power of 9 space h a s space u n i t space d i g i t space 3 3 to the power of 10 space h a s space u n i t space d i g i t space 9 . . . . .
Thus there is a pattern in the unit digit of powers of 3.
 
The unit digits are appearing in cylces of 3, 9, 7, and 1.
 
Therefore, if the power is divided by 4, and the remainder is 1, the unit digit is 3.
 
And, if the power is divided by 4, and the remainder is 2, the unit digit is 9.
 
And, if the power is divided by 4, and the remainder is 3, the unit digit is 7.
 
And, if the power is divided by 4, and the remainder is 0, the unit digit is 1.
 
So let us divide the power 2013 by 4.
 
Thus, 2013 equals 503 cross times 4 plus 1
since the remainder is 1, we have the unit digit as 3.
Answered by | 26 Mar, 2014, 09:03: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
express 15.265 in p/q form?
Asked by nagalaxmidurgarao937 | 08 Apr, 2024, 01:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
The LCM of three numbers 28, 44, 132 is
Asked by sagarmishra | 14 Mar, 2024, 12:11: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
LCM of first 25 natural number
Asked by apekshab05918 | 15 Feb, 2024, 11:29: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
2+2÷2
Asked by mahanandaparameswar2 | 31 Jan, 2024, 06:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
if the hcf of 408 and 1032 is expressible in the form 1032m-408×5 , find m
Asked by sitalagrawal969 | 21 Jan, 2024, 11:48: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
log base 10(cos0⁰)
Asked by bhaskrraobhaskrrao | 18 Jan, 2024, 08:35: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
can two numbers have 18 as their hcf and 380 is their lcm
Asked by randhirpandey196 | 16 Jan, 2024, 03:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
HCF of two numbers is 27 and their Lem is 62 • If one of the number is 54. find the Second number
Asked by scs902692 | 11 Jan, 2024, 08:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
if a,b,c are rational such that a+b√2+c√3=0 then a+b+c=
Asked by reddyjaswamth | 10 Jan, 2024, 01:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Use division algorithm to find the hcf of 867and 255
Asked by dc5756069 | 09 Jan, 2024, 07:35: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×