Prof. Radcliffedradcli@inverhills.edu

INTRODUCTION TO PLACE VALUE AND WHOLE NUMBERS

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

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.

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.

MillionsColumn

Hundred

Thousands

Column

TenThousa

ndsColumn

Thousands

Column

Hundreds

ColumnTens

ColumnOnes

Column1,000,00

0 100,000 10,000 1,000 100 10 1

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 Words6 6,000,000 Six million0 0 Zero8 80,000 Eighty

thousand1 1,000 One thousand4 400 Four hundred5 50 Fifty9 9 Nine

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

One thousand = 1,000 = 103This 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

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

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

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

Which of these are whole numbers?

a) 27b) –14c) 0d) 3.6e) 1,000,000,001f) 2/5

Answer: a, c, e

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 million6 600,000 Six hundred thousand5 50,000 Fifty thousand4 4,000 Four thousand3 300 Three hundred2 20 Twenty1 1 One

Write the number 987,654,321 in words

Nine hundred eighty-seven million,six hundred fifty-four thousand,

three hundred twenty-one.

Six trillion, four hundred fifty million.

Write the number 6,000,450,000,000 in words.

Write the number 40,319 in expanded form.

40,000 + 300 + 10 + 9

Write the number using digits: Seventeen billion, two hundred eleven million.

17,211,000,000