convert decimal number 250.5 to base 3
Answers
Answer:
2505/300
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Answer:
Let's break the number down: 2*10^2 + 5 * 10^1 + 5 * 10^-1.
The way that I like to deal with bases is to do the same sort of setup as before, replacing the 10 with 7 or 3, depending on your base. Then, it's a matter of finding your most significant bit and going from there. Let's write out the places: 729 (3^6), 243 (3^5), 81 (3^4), 27 (3^3), 9 (3^2), 3 (3^1), 1 (3^0). You could go further, but that's probably all we need.
In the case of base 3, you have a 243 (3^5), with 7.5 left over. Now looking at the remainder, The 7 is easy, that's just 2*3^1 + 1*3^0, giving you thus far 100021.
But what about anything past the trinary point (can't be decimal, because it's base 3, so we use trinary; base 7 will use heptal)? The powers work the same way: 1/3 (3^-1), 1/9 (3^-2), 1/27 (3^-3), 1/81 (3^-4), 1/243 (3^-5), and so on. If you add these fractions to get to 1/2, you will actually end up with a repeating 1, because it will take until infinity to reach 1/2, which is equivalent to decimal 0.5. So, your final answer in base 3 is 100021.1111111111 with the 1 repeating.
You should be able to use the same sort of formula to get base 7. Hope this helps.