How do you convert a number to whatever base it indicates? For example: convert 252 base six to base five. I have tried posting for my teacher to help me, but he doesn't seem to get what I am asking. Can someone please explain the process and not just the answer? Thanks!!

Most of the time, you would convert numbers from "foreign" bases to base 10, then convert to the target base by division.

From a number in base n, we recognize that each digit from the right represents n^x, where x is the position from the right.

So 2526
= 2*6² + 5*6¹ + 2*6^0
= 72 + 30 + 2
= 10410

To convert 10210 to base 5, we divide by 5 successively and collect the remainders as digits from the right.
102/5=20R4
20/5=4R0
4/5=0R4
So 10210 = 4045

Thanks. How did it change from 104 base 10 to 102?

102ten to base 5 is not 404five it is 402five

102/5=20 r 2
20/5=4 r 0
4/5 =0 r 4
so that gives you 402five

To convert a number from one base to another, you need to understand the concept of place value. Each digit in a number represents a value based on its position or place.

Here's the step-by-step process to convert a number from one base to another:

1. Identify the place values in the given number: In a given number, the rightmost digit represents the units place, the next digit to the left represents the base raised to the power of 1, the next one represents the base raised to the power of 2, and so on.

For example, in the number 252 (base six), the rightmost digit is the units place, the next digit is the base (six) raised to the power of 1, and the leftmost digit is the base raised to the power of 2.

2. Calculate the decimal value of the given number: Multiply each digit by the corresponding power of the base and add them together. In our example (252 base six), you would calculate:
2 * 6^2 + 5 * 6^1 + 2 * 6^0 = 72 + 30 + 2 = 104 (decimal).

3. Convert the decimal value to the desired base: To convert the decimal value to another base, repeatedly divide the decimal number by the desired base and note down the remainders as the digits of the new base number.

For example, to convert the decimal 104 to base five:
104 ÷ 5 = 20 remainder 4 (rightmost digit in base five)
20 ÷ 5 = 4 remainder 0 (next digit)
4 ÷ 5 = 0 remainder 4 (leftmost digit)

So, 104 (decimal) is equivalent to 404 (base five).

In conclusion, to convert 252 (base six) to base five, we follow the above steps to find that the answer is 404.