Place Value (Number Sense)

Numbers are grouped in periods or families. The number families are ones, thousands, millions, etc. There are three places in each number family: ones, tens, and hundreds.

Each place is tens times as big as the place to its right. For example:

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
100,000 x 10 = 1,000,000	10,000 x 10 = 100,000	1,000 x 10 = 10,000	100 x 10 = 1,000	10 x 10 = 100	1 x 10 = 10

The standard form of a number is written in numbers. For example: 1,234,567.

The word name of a number is written in words. For example: one million two hundred thirty four thousand five hundred sixty seven.

Expanded notation is the number written as the amount of each place value added together. For example: 1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7.

You can also use a place value mat to create a model of a number. For example:

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones

Place value and the digit determine the size of the number. For example: a 9 in the tens place is smaller than a 1 in the hundreds place because 9 tens = 90 and 1 hundred = 100.

< (is less than), = (is equal to ), and > (is greater than) are symbols used when we compare amounts. For example: 635,763 > 243,836.

When you compare numbers you start all the way to the left in the highest place value. A good strategy to help you is if you turn a piece of lined paper sideways and use the lines to help you line up the numbers.

We use our number sense when we round numbers. Rounded numbers end in one or more zeroes. To round a numbers, underline the place you want to round to. Look at the place to the right. If the digit is 5 or more, round up to the next number. If it is less than 5, the number stays the same. Put zeroes in the places to the right of the underlined number. For example: 37 is rounded to 40 because the 7 to the right of the 3 is more than five. 21 is rounded to 20 because the 1 to the right of the 2 is less than 5.