In the base-10 (or decimal) system, all numbers use ten symbols, or "digits": 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

To understand how we name and write numbers, let's start with this simple question:

What is the difference between the two numbers below?

• 128
• 821

These numbers use the same digits, "1," "2," and "8," but they definitely don't represent the same number. Switching the digits around changes the value of a number. How does this work?

Two things make a number unique and meaningful:

1. The digits
2. The position of the digits in the number

1) the digits and 2) the position of the digits in the number. Each position in the number has a specific "weight," called the "place value." This simulation helps you review place value by switching from a number's standard form (how we usually write it) to its expanded form (how we decompose a number into sums of other numbers). We'll use a "place value chart" to do this. In this chart, numbers are represented pictorially:

• One little "unit cube" for "one",
• One vertical "rod" for "ten" (i.e. ten "ones")
• One "flat" square for "hundred" (i.e. hundred "ones" or ten "rods")
• One thick "cube" for "thousand" (i.e. one thousand "ones", or one hundred "rods", or ten "flats")

Type a number in the upper box or type digits in the place value chart.

Click on '+' to add an item, Click an item to remove it.