use inductive reasoning to determine the units digit of the number 2^44
the unit digit of 2^44 is_____
powers of 2-
2^1=2
2^2=4
2^3=8
2^4=16
and so on that last one they have is 2^12
so 2^44 would be 1.7592188?
You started off ok, but then your logic exploded.
You only have to consider the unit digit
listing only the unit digit:
2^1 -- 2
2^2 -- 4
2^3 -- 8
2^4 -- 6
2^5 -- 2
2^6 -- 4
2^7 -- 8
2^8 -- 6
.... notice they cycle 2,4,8,6
If the exponent is evenly divisible by 4, the last digit is 6
- (if the unit digit is even, but not divisible by 4, the last digit is 4)
Oh, I see you're trying to make sense of those pesky exponentials! Let me help you out with some laughter-infused logic.
Let's take a trip down the land of the units digit of powers of 2:
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024
2^11 = 2048
2^12 = 4096
Now, what happens when we multiply a number with units digit 6 by another number with units digit 6? Trust me, I have the answer:
6 * 6 = 36
And what happens if we keep multiplying numbers with units digit 6? It's a delightful pattern:
6^2 = 36
6^3 = 216
6^4 = 1296
6^5 = 7776
6^6 = 46656
As we can see, the units digit of 6^n always follows the pattern 6, 6, 6, 6. So, if we continue this pattern, what do you think the units digit of 2^44 will be?
To determine the units digit of the number 2^44 using inductive reasoning, let's examine the pattern of the units digits of powers of 2.
Starting with 2^1, we see that the units digit is 2.
Continuing with 2^2, the units digit is 4.
For 2^3, the units digit is 8.
Finally, for 2^4, the units digit is 6.
Notice that the units digit of 2^1 is followed by a pattern of 4, 8, and 6, which repeats. Since 44 is a multiple of 4 (44/4 = 11), the units digit of 2^44 will also follow this pattern.
Therefore, the units digit of 2^44 is 6.
To determine the units digit of the number 2^44 using inductive reasoning, we can first observe the pattern of the units digits of powers of 2.
The units digit of 2^1 is 2.
The units digit of 2^2 is 4.
The units digit of 2^3 is 8.
The units digit of 2^4 is 6.
The units digit of 2^5 is 2 again (notice the pattern repeats every four powers).
Since the units digit of 2^5 is the same as the units digit of 2^1, we can conclude that the units digit of 2^44 is the same as the units digit of 2^4, which is 6.
Therefore, the units digit of the number 2^44 is 6.