This document introduces place value and whole numbers. It defines whole numbers as non-negative integers (0, 1, 2, 3, etc.) and explains our base-10 number system. Place value is described as the value of each digit depending on its position (ones, tens, hundreds, etc.). Examples show writing numbers in expanded form and converting between digit and word forms. Large numbers like millions and billions are defined and related to exponents of 10. The key concepts of place value, digit value, and naming large numbers are demonstrated.

1. Prof. Radcliffe
dradcli@inverhills.edu
INTRODUCTION TO
PLACE VALUE AND
WHOLE NUMBERS

2. Objectives
 Identify whole numbers
 Give the value of each digit in a number
 Write a number in expanded form
 Write a number in words
 Write a number with digits instead of words
 Visualize large numbers

3. What is a whole number?
 The whole numbers (or counting numbers) are 0, 1, 2, 3, 4, etc.
 They do not include negative numbers or fractions.
 Our number system is based on the number 10 (decimal).
 We write all numbers using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
 The positions of the digits in a number determine the values of the
digits. This is called place value.

4. Place Value
The first digit on the right is in the ones column.
The next digit to the left of the ones column is in the tens column.
Each time we move to the left, the columns get 10 times bigger.
Millions
Column
Hundred
Thousands
Column
Ten
Thousands
Column
Thousands
Column
Hundreds
Column
Tens
Column
Ones
Column
1,000,000 100,000 10,000 1,000 100 10 1

5. Example: Place Value
• Find the value of each digit in the number 6,081,459.
• 6,081,459 = 6,000,000 + 80,000 + 1,000 + 400 + 50 + 9
• This is called expanded form.
Digit Value Words
6 6,000,000 Six million
0 0 Zero
8 80,000 Eighty thousand
1 1,000 One thousand
4 400 Four hundred
5 50 Fifty
9 9 Nine

6. Naming Large Numbers
One hundred twenty-three trillion,
four hundred fifty-six billion,
seven hundred eighty-nine million,
twelve thousand,
three hundred forty-five.
Trillions Billions Millions Thousands Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
1 2 3, 4 5 6, 7 8 9, 0 1 2, 3 4 5

7. One thousand = 1,000 = 103
This cube contains 1,000 magnetic
spheres (10 x 10 x 10 = 1,000).
A typical adult horse weighs about
1,000 pounds.
http://magneticles.com
http://flic.kr/p/6RNCmk

8. One million = 1,000,000 = 106
• One million is one thousand
thousands.
• This clear lucite case holds one million
pennies.
• The maximum takeoff weight of an
Airbus A380 is about one million
pounds.
http://www.kmoser.com/onemillionpennies/
http://en.wikipedia.org/wiki/File:A380_Emirates_A6-EDC.jpg

9. One billion = 1,000,000,000 = 109
• One billion is one thousand millions.
• The Golden Gate Bridge weighs about two billion pounds.
http://en.wikipedia.org/wiki/File:GoldenGateBridge-001.jpg

10. One trillion = 1,000,000,000,000 = 1012
• One trillion is one thousand billions.
• The distance to the nearest star (except the
Sun) is about 25 trillion miles.
• The total weight of all humans is about half a
trillion pounds. http://upload.wikimedia.org/wikipedia/commons/a/ac/Proxima_Centauri_2MASS_Atlas.jpg
http://www.theenvironmentalblog.org

11. Which of these are whole numbers?
a) 27
b) –14
c) 0
d) 3.6
e) 1,000,000,001
f) 2/5
Answer: a, c, e

12. Find the value of each digit
in the number 987,654,321.
Digit Value Words
9 900,000,000 Nine hundred million
8 80,000,000 Eighty million
7 7,000,000 Seven million
6 600,000 Six hundred thousand
5 50,000 Fifty thousand
4 4,000 Four thousand
3 300 Three hundred
2 20 Twenty
1 1 One

13. Write the number 987,654,321 in words
Nine hundred eighty-seven million,
six hundred fifty-four thousand,
three hundred twenty-one.

14. Six trillion, four hundred fifty million.
Write the number 6,000,450,000,000 in words.

15. Write the number 40,319 in expanded form.
40,000 + 300 + 10 + 9

16. Write the number using digits: Seventeen
billion, two hundred eleven million.
17,211,000,000