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4-digit numbers

Definitions


  • We can group 10 hundreds into 1 thousand:
    = \(10\) hundreds \(= 1\) thousand =
  • To count how many thousands, hundreds, tens, and ones there are, we can make a table:
    Thousands Hundreds Tens Ones
    1 2 4 3
    The table tells us we have 1 thousand, 2 hundreds, 4 tens, and 3 ones, which we can write in positional notation as \(1\,243\).

Definition Base 10 system
In the base 10 system, the place of a digit in a number determines its value. We can represent a number:
  • with digits: $$1\,243$$
  • in expanded form: $$\begin{aligned}[t] 1\text{ thousand }&+& 2\text{ hundreds }&+& 4\text{ tens }&+& 3\text{ ones }\\1\,000 &+& 200 &+& 40 &+& 3 \\\end{aligned}$$
  • with words:
    one thousand two hundred forty-three
  • in a table:
    Thousands Hundreds Tens Ones
    1 2 4 3
  • with cubes:

On the Number Line


  • A number line shows numbers like 0, 1, 2, 3, and so on in order.
  • Let’s make counting easier by counting by tens on our number line. Now we jump 10 at a time: 0, 10, 20, 30.

Definition Number Line
A number line is a line that shows numbers in order. Moving right adds by same number.