Question

the digit at unit's place of (117)³ is​

Answer 1

Answer:

3 is the correct answer.

Given:

(117)³

To find:

the digit at the unit's place of (117)³

Solution:

the cyclic table for 117 is the same as that for 7, i.e, 7, 9, 3, 1, and then back to 7.

• the unit digit for 117 x 117 would be the same as 7x7= 49 i.e., 9.

• when we further cube this, we will be multiplying 117 by a number that ends with 9. so, the unit digit for that will be the same as 7 x 9= 63, i.e., 3.

• since the power of 117 is 3, the unit digit would be 3.

• for powers 1, 2, 3, and 4, the unit digit would be  7, 9, 3, and 1 respectively.

Hence, 3 is the correct answer.

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Answer 2

Answer:

The answer to the given question is 3.

Step-by-step explanation:

Given

(117)³

To find :

The unit's place of the given expression.

Solution :

The cube of 117 can be calculated by multiplying the same number twice

$117 \times 117 \times 117 = 13689 \times 117 = 1601613$

The digit at the unit's place is 3.

It is difficult for us to multiply the larger number three times. so we can move on to some basic logic.

As the unit digit in the number is 7.

The cyclic table for 117 will be the same as that for 7.

I.e., 7,9,3,1 again it will be back to 9.

The unit for 117*117 and 7*7 will be the same.

which is 9

then further multiplying them with the same number to make it a cube which is multiplying the number 117 by the number that ends with 9.

The unit digit for that will be 3.

Therefore, the power of 117 is also 3 and the value at the unit's place is 3.

It is given that for the powers 1,2,3 and 4 of the given number, the value of the digit at the unit's place will be 7,9,3 and 1 respectively.

The correct answer to the given question is 3.

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