Base 10 Place Value

Our place value system is based on 10's. Ten 1's = One 10, Ten 10's = One 100, etc. We can also think of our place value system in powers of 10.

WHOLE NUMBER PLACE VALUE DEFINITION: The whole numbers are the numbers 0, 1, 2, 3, ... A digit is any of the numbers 0,1,2,3,4,5, 6,7,8, or 9. The value of each digit in a whole numbers depends on its position within the number. For example, in the whole number 127,891, the 8 has a value of 800 because it is in the hundreds' place and 8 x 100 = 800. Each number is 10 times the value to the right of it, hence the term base ten. The numbers continue indefinitely in this pattern: 100000,10000,1000,100,10,1 0.1, 0.01, 0.001, 0.0001, 0.00001.

Example 1:

Write the number 74,608 in expanded form. Expanded form is when you multiply each digit by it's place value and add all the values together.

74,608 = 70,000 + 4,000 + 600 + 8

7 x 10,000 + 4 x 1,000 + 6 x 100 + 8 x 1 = 74,608

Note: The zero in the tens' place is a placeholder.

Example 2:

Write the number in standard form. Standard form is when the number is written in the normal way.

90,000 + 1,000 + 300 + 60 = 91,360

91, 360 is the standard form.

9 x 10,000 + 1 x 1000 + 3 x 100 + 6 x 10 = 91,360

Guided Practice Problems:

1. 8 hundreds = ? tens

2. 7 thousands = ? hundreds

3. 9 ten thousands = ? thousands

4. Write the number 68,237 in expanded form.

5. Write the number in standard form:

3 x 100,000 + 6 x 10,000 + 5 x 1,000 + 4 x 100 + 8 x 10 + 1

6. In 16,482 which number is in the thousands place?

7. In 24,386 which number is in the ten thousands place?