Tonight's Math Homework

Base 3

We're still trying to get a solid grip on place value. Since you guys have been working with base 10 for so long, to clear up any misunderstandings we're shaking it up a bit. Enter: Triopolis. Where triopolans ride around on tricycles and sit on tripods and their national sport is triathlons. So, their money system is base 3. 

Looking at the picture below, the yellows equal 1 (that's because any time we count anything we start at 1). But, in base-3: 

• 3 yellows = 1 blue; 
• 3 blues = 1 green 
• (so, if one green equals 3 blues and each blue equals 3 yellows, then 1 green = 9 yellow).  
• 3 green = 1 Red (27 yellow)

So, if we go to triopolis with $8 american dollars, we would trade it for 2 triopolan blues (equaling 6) and 2 yellows. And we'd write that 22 and to show that we mean 2 blues, 2 yellows we would put a lowered exponent 3 right next to the 22. 

The number above 1012 in base 3 = 1 Red (27) + 0 Green + 1 Blue (3) + 2 Yellow (2). For a total of 32 in Base 10. 

I hope this explanation helps you and your parents work solving the problems tonight. If you have any questions or are having any trouble remember, all I ask is 15-20 minutes of solid effort!