66 in base 12 + 9+9 in base 12 + 48 in base 12
To add numbers in different bases, you need to convert all numbers to the same base. Here, we need to convert 66 from base 12 to base 10, as well as convert 9+9 from base 12 to base 10.
To convert 66 from base 12 to base 10, we can use the place value system.
66 in base 12 = (6 * 12^1) + (6 * 12^0)
= (6 * 12) + (6 * 1)
= 72 + 6
= 78
To convert 9+9 from base 12 to base 10:
9 + 9 in base 12 = (9 * 12^0) + (9 * 12^0)
= 9 + 9
= 18
Now that we have converted both numbers to base 10, we can add them together.
78 + 18 = 96
Hence, 66 in base 12 + 9+9 in base 12 + 48 in base 12 is equal to 96.
To add these numbers in base 12, we need to convert each number to decimal, perform the addition, and then convert the result back to base 12.
First, let's convert each number to decimal:
66 in base 12 = (6 * 12^1) + (6 * 12^0) = 72 + 6 = 78
9+9 in base 12 = (9 * 12^0) + (9 * 12^0) = 9 + 9 = 18
48 in base 12 = (4 * 12^1) + (8 * 12^0) = 48 + 8 = 56
Now, let's add these decimal numbers:
78 + 18 + 56 = 152
Finally, let's convert the sum back to base 12:
152 = (12^2) + (2 * 12^1) + (8 * 12^0) = 1028 in base 12
So, the sum of 66 in base 12 + 9+9 in base 12 + 48 in base 12 is 1028 in base 12.
To perform addition in different number bases, each number must be converted to the same base before adding them together. Let's convert all the numbers to base 10 first, then perform the addition, and finally convert the result back to base 12.
1. Converting 66 from base 12 to base 10:
To convert a number from base 12 to base 10, we multiply each digit by the corresponding power of 12, starting from the rightmost digit. For 66 in base 12, the rightmost digit (6) will be multiplied by 12^0, and the leftmost digit (6) will be multiplied by 12^1.
66 in base 12 = (6 * 12^1) + (6 * 12^0) = 72 + 6 = 78 in base 10.
2. Converting 9+9 from base 12 to base 10:
Similarly, for 9+9 in base 12, we convert each digit separately. In base 12, the rightmost digit (9) will be multiplied by 12^0, and the leftmost digit (9) will be multiplied by 12^1.
9+9 in base 12 = (9 * 12^1) + (9 * 12^0) = 108 + 9 = 117 in base 10.
3. Converting 48 from base 12 to base 10:
Again, we convert each digit separately:
48 in base 12 = (4 * 12^1) + (8 * 12^0) = 48 + 8 = 56 in base 10.
Now, we can add the three base 10 numbers together: 78 + 117 + 56 = 251.
Finally, let's convert the result back to base 12:
To convert a number from base 10 to base 12, we divide the number by 12 repeatedly until the quotient is 0, and then we take the remainders in reverse order to form the base 12 representation.
251 in base 12 = 20 remainder 11 in base 12.
The remainder 11 corresponds to the digit 'B' in base 12.
Therefore, the final answer is "20B" in base 12.