# Representing Numbers

## Learning Goal:

I will be able to...

• represent, compare and order numbers
Place Value Song (Rude by MAGIC! Parody)

## Place Value

What makes a number mean what it does? Is it simply the digits in the number? For example, let's consider the number 521.

If we switch the digits around, we might get 125. Definitely not the same number. So, it's not just the digits that make a number; it's the digits and their positions within the number. A digit's position in a number and its resulting value is called place value.

## Expanded Form

When we write the number 521, what that number really means is that we have the total of 500 + 20 + 1. We've expanded the number to show the value of each of its digits. When we expand a number to show the value of each digit, we're writing that number in expanded form.

Let's try it with a different, bigger number: 1,234,567. We'll start by placing the number's digits in the place value chart.

Since the 1 is in the millions place, it means one million, or 1,000,000

Since the 2 is in the hundred thousands place, it means two hundred thousands, or 200,000

Since the 3 is in the ten thousands place, it means three ten thousands, or 30,000

Since the 4 is in the thousands place, it means four thousands, or 4,000

Since the 5 is in the hundreds place, it means five hundreds, or 500

Since the 6 is in the tens place, it means six tens, or 60

Since the 7 is in the ones place, it means seven ones, or 7

If we write the number 1 234 567 in expanded form it would be:

1 000 000 + 200 000 + 30 000 + 4 000 + 500 + 60 + 7