 WME@Kimpton Middle

## Place Values

What about writing down larger numbers? One way is to create more symbols. For example, these Chinese numerals are in use today.

 十 百 千 万 ten hundred thousand ten thousand

But we can't create new symbol to keep up with ever larger numbers. An ingeneous solution is to use the place value system described here. To write down numbers larger than 9, we place two numerals side by side. The numeral on the right is in the ones place and the numeral to its left is in the tens place. For example,

37 = three tens and seven ones

Or we can state it in another way.

3 × 10 + 7 × 1

1. What is the largest number you can write with two places?

2. The next places to the left are the hundreds, thousands, and so on, as shown in the diagram above.

What is the largest number you can write with three places?

3. What is the largest number you can write with four places?

4. Pick one:

5. Now, generate a number:

6. For this number you just generated, fill in these blanks.
Ones place =    Tens place =    Hundreds place =    Thousands place =

7. And fill in these blanks.
= × 1 + × 10 + × 100 + × 1000

In summary, the place value system allows us to use just the ten numerals to write down any integer no matter how big.

To further understand the place value notation, experiment with this counter. It adds one to the position you click and carry to the next higher position.

As you count up repeatedly on one position, you'll see how it carries to the next position.

Now, generate a counter that counts down when you click:

As you count down repeatedly on one position, you'll see how it borrows from the next position.