Answer:
Commutative Property
Step-by-step explanation:
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
Answer:
A
Step-by-step explanation:
A pictograph displays pictures to represent information
Answer:
The answer would be 2.9
Step-by-step explanation:
its already rounded
Writing numbers in base 10 means to write them as a combination of powers of 10, for example
![1925 = 1\cdot 10^3 + 9\cdot 10^2 + 2\cdot 10^1+5\cdot 10^0](https://tex.z-dn.net/?f=1925%20%3D%201%5Ccdot%2010%5E3%20%2B%209%5Ccdot%2010%5E2%20%2B%202%5Ccdot%2010%5E1%2B5%5Ccdot%2010%5E0)
So, writing numbers in any base means to do the same thing: for example, in base 3, we have
![102_3 = 1\cdot 3^2 +0\cdot 3^1 +2\cdot 3^0 = 12_{10}](https://tex.z-dn.net/?f=102_3%20%3D%201%5Ccdot%203%5E2%20%2B0%5Ccdot%203%5E1%20%2B2%5Ccdot%203%5E0%20%3D%2012_%7B10%7D)
So, in order to write 80 in base 3, we have to find out the largest power of 3 that fits: we have
![3^0=3,\ \ 3^1=3,\ \ 3^2=9,\ \ 3^3=27,\ \ 3^4=81](https://tex.z-dn.net/?f=3%5E0%3D3%2C%5C%20%5C%203%5E1%3D3%2C%5C%20%5C%203%5E2%3D9%2C%5C%20%5C%203%5E3%3D27%2C%5C%20%5C%203%5E4%3D81)
So, since
is too much, our number will have 4 digits:
![abcd_3 = a\cdot 3^3 +b\cdot 3^2 +c\cdot 3^1 + d\cdot 3^0](https://tex.z-dn.net/?f=abcd_3%20%3D%20a%5Ccdot%203%5E3%20%2Bb%5Ccdot%203%5E2%20%2Bc%5Ccdot%203%5E1%20%2B%20d%5Ccdot%203%5E0)
In order to find the digits, again we see "how much it fits": we have
![0\cdot 3^3 = 0\ \ 1\cdot 3^3 = 27,\ \ 2\cdot 3^3 = 54](https://tex.z-dn.net/?f=0%5Ccdot%203%5E3%20%3D%200%5C%20%5C%201%5Ccdot%203%5E3%20%3D%2027%2C%5C%20%5C%202%5Ccdot%203%5E3%20%3D%2054)
So, we choose
. The remainder is ![80-54=26](https://tex.z-dn.net/?f=80-54%3D26)
Now we need to fix the coefficient for
: we have
![0\cdot 3^2 = 0\ \ 1\cdot 3^2 = 9,\ \ 2\cdot 3^2 = 18](https://tex.z-dn.net/?f=0%5Ccdot%203%5E2%20%3D%200%5C%20%5C%201%5Ccdot%203%5E2%20%3D%209%2C%5C%20%5C%202%5Ccdot%203%5E2%20%3D%2018)
Again we choose ![b=2](https://tex.z-dn.net/?f=b%3D2)
Keep going like this and you'll find out that
![80_3 = 2222](https://tex.z-dn.net/?f=80_3%20%3D%202222)
This was actually a special case, because our number is exactly one less than a power of 3: we have
![80=3^4-1](https://tex.z-dn.net/?f=80%3D3%5E4-1)
and just like in base 10, when we subtract 1 from a power of 10 we get a number composed by 9 only:
![10000000-1 = 9999999](https://tex.z-dn.net/?f=10000000-1%20%3D%209999999)
In every base, when we subtract 1 from a power of the base we get a number composed by (base-1) only:
![(10000-1)_3 = 2222](https://tex.z-dn.net/?f=%20%2810000-1%29_3%20%3D%202222)