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**Introduction to place value and whole numbers**

Prof. Radcliffe

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**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

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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.

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**Hundred Thousands Column**

Place Value 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 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.

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

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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 1 2 3, 4 5 6, 7 8 9, 2, 3

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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. Image Source:

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**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.

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One billion = 1,000,000,000 = 109 One billion is one thousand millions. The Golden Gate Bridge weighs about two billion pounds.

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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.

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**Which of these are whole numbers?**

27 –14 3.6 1,000,000,001 2/5 Answer: a, c, e

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**Find the value of each digit in the number 987,654,321.**

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 One

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**Write the number 987,654,321 in words**

Nine hundred eighty-seven million, six hundred fifty-four thousand, three hundred twenty-one.

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

Six trillion, four hundred fifty million.

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**Write the number 40,319 in expanded form.**

40,

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

17,211,000,000

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