divide in the indicated base
2 base 3/ 120 base 3
To divide in a specific base, you need to perform the division operation using the rules of that base. In this case, we have a division problem in base 3.
To divide 2 (in base 3) by 120 (in base 3), we'll follow these steps:
Step 1: Set up the division problem:
Place the dividend (2) inside the division symbol (÷) and the divisor (120) outside.
```
0. (quotient)
_____
120 | 2
```
Step 2: Determine the largest multiple of the divisor that is less than or equal to the dividend in that base. In this case, we are in base 3.
The largest multiple of 120 (in base 3) that is less than or equal to 2 (in base 3) is 1 (in base 3).
Step 3: Write down the value of the largest multiple found (1) above the division symbol (÷), as the first digit of the quotient.
```
0. 1 (quotient)
_____
120 | 2
```
Step 4: Multiply the divisor by the value written above the division symbol, and write the result below the dividend.
```
0. 1 (quotient)
_____
120 | 2
- 0 (result of 120 * 1)
```
Step 5: Subtract the result of Step 4 from the dividend.
2 (in base 3) - 0 (in base 3) = 2 (in base 3)
Step 6: Bring down the next digit of the dividend.
As we don't have any more digits in the dividend, we have completed the division process.
Therefore, in base 3, 2 ÷ 120 equals 0.1.
Please note that in base 3 (ternary), the digit "2" doesn't exist. It only uses the digits 0, 1, and 2, but since the divisor is 120 (in base 3), which is greater than the dividend (2 in base 3), the quotient will be 0.1.