a. How many cartons of milk would this be in base ten?

  

    b. Which of the six characteristics of base ten (on page 101) does this system possess? Justify your responses. 

  

    Base ten  

  

    1. Any base has only one-zero symbols. With those one-zero symbols, we can represent any amount; think of Toy Story—“to infinity and beyond!”

  

    2. The value of each place is one-zero times the previous place.

  

    3. Each place can contain only one symbol. When a place is full, we “move” to the next place by regrouping (exchanging) 10 of the given place to 1 of the next higher place.

  

    4. The value of a digit depends on its place in the numeral.

  

    5. The value of a numeral is determined by multiplying each digit by its place value and then adding these products.

  

    6. Zero represents an empty place and 0 represents an actual amount, with a place on the number line.

In some dairy states, a kind of base 6 is used for shipping milk. Six cartons of milk make 1 box; 6 boxes make 1 crate, 6 crates make 1 flat, and 6 flats make 1 pallet. Thus, if someone said they had filled 4355, that would mean 4 flats, 3 crates, 5 boxes, and 5 cartons.