Calculate 243 base six minus 243 base five, expressing your answer in base ten
243₆ = 2 ∙ 6² + 4 ∙ 6¹ + 3 ∙ 6⁰ = 2 ∙ 36 + 4 ∙ 6 + 3 ∙ 1 = 72 + 24 + 3 = 99₁₀
243₅ = 2 ∙ 5² + 4 ∙ 5¹ + 3 ∙ 5⁰ = 2 ∙ 25 + 4 ∙ 5 + 3 ∙ 1 = 50 + 20 + 3 = 73₁₀
243₆ - 243₅ = 99 - 73 = 26
Well, I have to say, working with different bases can be a bit puzzling. It's like trying to decipher a secret code, but let's give it a shot!
To tackle this, let's first convert both numbers to base ten.
243 base six is actually 2*(6^2) + 4*(6^1) + 3*(6^0), which equals 87 in base ten.
243 base five is 2*(5^2) + 4*(5^1) + 3*(5^0), which equals 68 in base ten.
Now, let's subtract those two numbers: 87 - 68 = 19.
So, 243 base six minus 243 base five, expressed in base ten, is 19.
Remember to always have a good laugh while doing math!
To calculate 243 base six minus 243 base five and express the answer in base ten, we need to convert both numbers to base ten and then subtract them.
First, let's convert 243 base six to base ten:
243 base six means (2 * 6^2) + (4 * 6^1) + (3 * 6^0)
= (2 * 36) + (4 * 6) + (3 * 1)
= 72 + 24 + 3
= 99 base ten
Next, let's convert 243 base five to base ten:
243 base five means (2 * 5^2) + (4 * 5^1) + (3 * 5^0)
= (2 * 25) + (4 * 5) + (3 * 1)
= 50 + 20 + 3
= 73 base ten
Now, we can subtract the two base ten numbers:
99 (base ten) - 73 (base ten) = 26 (base ten)
Therefore, 243 base six minus 243 base five is equal to 26 in base ten.
To calculate 243 base six minus 243 base five and express the answer in base ten, we need to convert both numbers to base ten and subtract them.
To convert a number from base six to base ten, each digit is multiplied by the corresponding power of six and summed. Let's convert 243 base six to base ten:
243 base six = (2 * 6^2) + (4 * 6^1) + (3 * 6^0)
= (2 * 36) + (4 * 6) + (3 * 1)
= 72 + 24 + 3
= 99
Now let's convert 243 base five to base ten:
243 base five = (2 * 5^2) + (4 * 5^1) + (3 * 5^0)
= (2 * 25) + (4 * 5) + (3 * 1)
= 50 + 20 + 3
= 73
Now subtract the base ten equivalents:
99 - 73 = 26
Therefore, 243 base six minus 243 base five, expressed in base ten, is equal to 26.