Decomposing numbers

In base 10 (also called decimal system), all the numbers we handle use 10 symbols or "digits": 0,1,2,3,4,5,6,7,8,9

In order 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?

What makes a number unique and meaningful is two things:

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

Each position in the number has a specific "weight" which is called the "place value". This simulation helps you to review the place value by switching from the standard form of a number (how we usually write it) to its expanded form (how we decompose this number in sums of others). We'll focus on the "place value chart" to achieve this. In this chart, numbers will be 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.

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