+0

# how do you do these?

+1
28
4
+403

What is the units digit of 2^2010?

how r u supposed to do these

Oct 13, 2020

#1
0

The last 10 digits of 2^2010 =...........6606081024

Note: Somebody should give you a short-cut to this computation.

Oct 13, 2020
#2
+403
+1

yeah i want to know how to do it thx though

Oct 13, 2020
#3
+1

Notice that 2n for n = 1 • • •  the value of 2n is as follows:

2,         4,         8,       16,

32,       64,     128,     256,

512,   1024,   2048,   4096,

8192, 16384, 32768, 65536,

etc.

The units digit repeats after every four exponents.

Example:  Say you wanted to know 27 ... divide the 7 by 4 and the remainder is 3.

So the units digit will be the third one in the repeating groups, which is 8.

Example:  Or, you wanted to know 216 ... divide the 16 by 4 and the remainder is 0.

But when a remainder is 0, that's the same as it being the same as the divisor, which was 4.

So the units digit will be the fourth one in the repeating groups, which is 6.

Okay, skip ahead to 22010 ... divide the 2010 by 4 and the remainder is 2.

That means the units digit will be the second one in the repeating groups, which is 4

.

Oct 13, 2020
#4
+403
+1

I get it, thank you sooooooo much

Oct 14, 2020