If 3245 base six =X base nine find X
To convert a number from base six to base nine, we need to first convert it to base ten, and then convert it to base nine.
Given that 3245 is a number in base six, we can convert it to base ten by multiplying each digit by the corresponding power of six and summing the results:
3*6^3 + 2*6^2 + 4*6^1 + 5*6^0 = 648 + 72 + 24 + 5 = 749
Now, we need to convert 749 from base ten to base nine.
To do that, we divide 749 by 9 and keep track of the remainders until we reach 0.
749 ÷ 9 = 83 remainder 2
83 ÷ 9 = 9 remainder 2
9 ÷ 9 = 1 remainder 0
1 ÷ 9 = 0 remainder 1
Reading the remainders from bottom to top, we have 1022 in base nine.
Therefore, 3245 base six = 1022 base nine.
To convert a number from one base to another, we need to convert it to base 10 first, and then convert it to the desired base.
In this case, we have "3245" in base six. To convert it to base 10, we can use the following steps:
1. Start from the rightmost digit and multiply each digit by the base raised to the power of its position. For base six, the positions are: 0 (rightmost), 1 (next to the left), 2 (next to the left), and so on.
So, we have:
5 * 6^0 = 5 * 1 = 5
4 * 6^1 = 4 * 6 = 24
2 * 6^2 = 2 * 36 = 72
3 * 6^3 = 3 * 216 = 648
2. Add up all the results from step 1.
5 + 24 + 72 + 648 = 749
So, "3245" in base six is equal to 749 in base 10.
Now, we need to convert 749 from base 10 to base nine. To do this, we can use the following steps:
1. Divide 749 by 9 and keep track of the remainders.
749 ÷ 9 = 83 remainder 2
83 ÷ 9 = 9 remainder 2
9 ÷ 9 = 1 remainder 0
1 ÷ 9 = 0 remainder 1
2. Write down the remainders in reverse order. The last remainder is the leftmost digit and the first remainder is the rightmost digit.
So, we have: 1022 in base nine.
Therefore, if 3245 base six = X base nine, then X = 1022.
To find the value of X in base nine, we first need to convert the number 3245 from base six to base ten, and then convert the resulting base ten number to base nine.
Step 1: Convert from base six to base ten
To convert a number from base six to base ten, we need to multiply each digit of the number by the corresponding power of six and sum up the results.
In this case, the number is 3245 base six. Breaking it down by place value, we have:
3 * 6^3 + 2 * 6^2 + 4 * 6^1 + 5 * 6^0
Calculating the powers of six:
6^3 = 216
6^2 = 36
6^1 = 6
6^0 = 1
Multiplying the corresponding digits by the powers of six:
3 * 216 + 2 * 36 + 4 * 6 + 5 * 1
Simplifying the equation:
648 + 72 + 24 + 5 = 749
Therefore, 3245 base six is equal to 749 base ten.
Step 2: Convert from base ten to base nine
To convert a number from base ten to base nine, we need to repeatedly divide the base ten number by nine and record the remainders.
Starting with the number 749 base ten, we perform the following divisions:
749 divided by 9 equals 83 with a remainder of 2.
83 divided by 9 equals 9 with a remainder of 2.
9 divided by 9 equals 1 with a remainder of 0.
1 divided by 9 equals 0 with a remainder of 1.
Reading the remainders in reverse order, the base nine representation of 749 base ten is 1022.
Therefore, X equals 1022 base nine.