What is a base-10 number system? Copyright 2010 Sopris West Educational Publisher

We know our number system is a base-10 number system that can be shown on a place-value chart. Copyright 2010 Sopris West Educational Publisher

Let's look at the number nine hundred sixty-eight thousand, two hundred fifty-three. Copyright 2010 Sopris West Educational Publisher

We can see the digit 9 represents 900,000, or 9 times 100,000. Copyright 2010 Sopris West Educational Publisher

The six represents 60,000 or 6 times 10,000. Copyright 2010 Sopris West Educational Publisher

The eight represents 8,000 or 8 times 8,000. Copyright 2010 Sopris West Educational Publisher

The two represents 200 or 2 times 100. Copyright 2010 Sopris West Educational Publisher

The 5 represents 50 or 5 times 10. Copyright 2010 Sopris West Educational Publisher

The 3 represents 3 ones, or 3 times 1. Copyright 2010 Sopris West Educational Publisher

How do we break down numbers to powers of 10? Copyright 2010 Sopris West Educational Publisher

A systematic way to break down a number to a power of 10 is to break it down to 10s, hundreds, and thousands.

When breaking down 1,000 into powers of ten, it can be broken down as 100 times 10…

…or 10 times 100…

…or 1 times 1,000.

When we break down 7,000 to a power of 10, it can be broken down as 700 times 10…

…or 70 times 100…

…or 7 times 1,000.

When we break down 9,000 to a power of 10, it can be broken down to 900 times 10…

…or 90 times 100…

…or 9 times 1,000. Each number can be divided by a power of 10 with no remainder.

Understanding the place value system helps when you are regrouping Understanding the place value system helps when you are regrouping. Because we are working in a base-10 system, we regroup when we have a group of 10 in any one place value position.

We first look at the ones place. This chart shows ten ones…

…regrouped into one 10.

We also regroup when we have a group of 10 in the tens place.

This table shows ten tens…

…regrouped into one hundred.