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5-digit numbers

Definitions


  • When we have 10 ones=, we group them into 1 ten=.
  • When we have 10 tens=, we group them into 1 hundred=.
  • When we have 10 hundreds = , we group them into 1 thousand =
  • When we have 10 thousands = , we group them into 1 ten thousand=
  • To count how many ten thousands, thousands, hundreds, tens, and ones there are, we can make a table:
    Ten Thousands Thousands Hundreds Tens Ones
    1 2 1 2 3
    The table tells us we have 1 ten thousands, 2 thousands, 1 hundred, 2 tens, and 3 ones, which we can write in positional notation as \(12\,123\).

Definition Base 10 system
In the base 10 system, the place of a digit in a number determines its value. We can represent the number \(32\,354\) in several ways:
  • With digits: $$32\,354$$
  • In expanded form:$$\begin{aligned}[t]3\text{ ten-thousands } &+ &2\text{ thousands } &+ &3\text{ hundreds } &+ &5\text{ tens } &+ &4\text{ ones }\\30\,000 &+ &2\,000 &+ &300 &+ &50 &+ &4 \\3\times 10\,000&+& 2\times 1\,000&+& 3\times 100&+&5\times 10&+&4\times 1\\\end{aligned}$$
  • With words:
    thirty-two thousand three hundred fifty-four
  • In a table:
    Ten-Thousands Thousands Hundreds Tens Ones
    3 2 3 5 4
  • 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.