Question

Find the unit digit of the number 17^2003.
Select one:
a. 7
b. 9
c. 3
d. 1

Answer 1

Answer:

3

Step-by-step explanation:

cyclicity of 7 = 4

so , 2003 ÷ 4

which will give you

Quotiont = 50

Reminder = 3

50+3 = 53

units place "3"

Answer 2

Given:

A number in exponential form$17^{2003}$.

To Find:

The units digit of the above number.

Solution:

1. The given number is 17^2003.

2. The number$17^{2003}$ can be also written as,

=>$17^{2003}$ = $(10^{2003} +7^{2003} )$,

3. The units digit of the number$10^{2003}$ is 0. ( All the powers of 10 end with 0 except 10^0 which ends with 1 ).

4. The units digit value  of 7^n is,

• 7 for 4n+1 type values, (n can vary from 0 to infinite)
• 9 for 4n+2 type values,
• 3 for 4n+3 type values,
• 1 for 4n type values.

For example, the units digit of 7³ is 3 as 3 can be also written as 4(0) +3.

5. Using the property mentioned above the units digit of the number$17^{2003}$ can be found,

=> 2003 = 4(500) + 3, ( 4n + 3 type value)

=> Therefore, the units digit is 3.

Therefore, the units digit of the number 17^2003 is 3. Option C is the correct answer.