Convert the number to the indicated base.
53six to base three
53base 6 is 3+5*6 base 10 or 33base10
base2: mirror image 0201 or 1020 .
check: 0*1+3*2+0*9+1*27
53base6=1020base3
53six to base three
3*6^0 + 5*6^1 = 33 decimal
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
1*27 + 0*9 + 2*3 + 0*1
1 0 2 0
Sure, let me clown around and convert it for you!
To convert 53six (also known as 5 in base 6 and 3 in base 10) to base three, we'll divide the number by 3 repeatedly until we reach zero.
Let's go through the process step by step:
53 divided by 3 is 17 with a remainder of 2 (that's a bit odd, isn't it?).
17 divided by 3 is 5 with a remainder of 2 (oh, what a coincidence!).
5 divided by 3 is 1 with a remainder of 2 (this is getting repetitive!).
1 divided by 3 is 0 with a remainder of 1 (and we finally reach zero).
Now, we'll take the remainders from the bottom up, and that gives us our converted number. So in base three, 53six would be represented as 2212. Ta-da!
Hope I managed to tickle your funny bone with this clownish answer. If you have any more questions, feel free to ask!
To convert the number 53six to base three, we first need to determine the equivalent value of each digit in base ten. Since the "six" digit is in base six, we can replace it with the value 6.
53six = 5 * (6^1) + 3 * (6^0)
Next, convert each digit to base ten:
5 * (6^1) = 5 * 6 = 30
3 * (6^0) = 3 * 1 = 3
Now, add these values together:
30 + 3 = 33
So, the number 53six in base three is equal to 33.
To convert a number from one base to another, you need to follow these steps:
1. Determine the value of each digit in the original number.
The original number "53six" has two digits: 5 and 3. The digit 5 is in the base 6's 10's place, while the digit 3 is in the 1's place.
2. Convert each digit of the original number to its decimal value.
In base 6, the decimal equivalent of the digit 5 is 5, and the decimal equivalent of the digit 3 is 3.
3. Multiply each decimal digit by the power of the original base corresponding to its position.
In this case, the digit 5 in the 10's place should be multiplied by 6^1, and the digit 3 in the 1's place should be multiplied by 6^0.
Calculation:
- Digit 5: 5 * 6^1 = 30
- Digit 3: 3 * 6^0 = 3 * 1 = 3
4. Add all the results together to get the decimal value of the original number.
In this case, 30 + 3 = 33 (the decimal value of "53six" in base 10).
5. Convert the decimal value to the desired base.
To convert the decimal value of 33 to base three, divide the number by 3 repeatedly until the quotient is zero, and record the remainders.
Calculation:
- 33 ÷ 3 = 11 remainder 0
- 11 ÷ 3 = 3 remainder 2
- 3 ÷ 3 = 1 remainder 0
- 1 ÷ 3 = 0 remainder 1
6. The converted number is formed by writing the remainders from step 5 in reverse order.
In this case, the remainders are 1, 0, 2, 0, reading from bottom to top.
Therefore, "53six" in base six converted to base three is "1020".