Question

find number of digits in a number raised to power

Answer 1

What is a Units digit?

Units digit of a number is the digit in the one’s place of the number. i.e It is the rightmost digit of the number. For example, the units digit of 243 is 3, the units digit of 39 is 9.

But then what is the units digit of large numbers like 23 to the power 46 or what is the units digit of 2014 to the power of 2014? Here, it is not straight forward to calculate the units digit of these numbers. So lets have a look at the technique to calculate the units digit of large numbers.

Units digit of Large Numbers – number raised to power

One of the ways of finding the units digit of a power is by finding the remainder when that number is divided by 10.
Another general and one of the easier ways to find the units digit of a number in the form
x
y
xy, is done with the help of the following steps:

Identify the units digit in the base ‘x’ and call it say ‘l’. {For example, If x = 24, then the units digit in 24 is 4. Hence l = 4.}
Divide the exponent ‘y’ by 4.
If the exponent y is exactly divisible by 4. i.e, y leaves a remainder 0 when divided by 4. Then,
the units digit of
x
y
xy is 6, if l = 2, 4, 6, 8.
the units digit of
x
y
xy is 1, if l = 3, 7, 9.
If y leaves a non-zero remainder r, when divided by 4 (i.e y = 4k + r). Then,