Basic Mathematics

Lawrence A. Trivieri

• Publisher: Collins Reference
• Year: 2011
• ISBN:
  9780062115058
• Topic: Studienhilfen
• Subtopic: Erweiterte Platzierung

Master Your Coursework with Collins College Outlines

From fraions, decimals, and geometric measurement to exponents, scientific notation, and an introduion to algebra, the Collins College Outline in Basic Mathematics explores and explains the topics that students will find in introduory mathematics classes. Completely revised and updated by Dr. Lawrence Trivieri, Basic Mathematics includes a test yourself seion with answers and complete explanations at the end of each chapter. Also included are bibliographies for further reading, as well as numerous graphs, charts, and example problems.

The Collins College Outlines are a completely revised, in-depth series of study guides for all areas of study, including the Humanities, Social Sciences, Mathematics, Science, Language, History, and Business. Featuring the most up-to-date information, each book is written by a seasoned professor in the field and focuses on a simplified and general overview of the subje for college students and, where appropriate, Advanced Placement students. Each Collins College Outline is fully integrated with the major curriculum for its subje and is a perfe supplement for any standard textbook.

CHAPTER I

The Whole Numbers

In this chapter, we consider the whole numbers, together with the arithmetic operations on them. Various properties associated with these operations and ordering of the whole numbers are also examined. Applications involving whole numbers are included throughout the chapter.

1.1 NUMBERS, NUMERALS, COUNTING, AND PLACE VALUE

In this section, we discuss the value of each digit in a numeral, write the word name for a number, and write the numeral for the word name of a number.

NUMERALS

Counting involves the use of only ten symbols or numerals called digits. These are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The counting numbers from 1 through 9 involve a single digit. The numbers from 10 through 99 have two digits. The numbers from 100 through 999 have three digits, and so on.

As the numbers get larger, we need longer numerals to represent them. The digits in longer numerals are separated by commas into groups of three, such as 759,189,304.

PLACE VALUE

Each digit has place value. The location of a digit in a numeral indicates the value of the digit. Starting from the right and moving to the left, the digits represent ones, tens, hundreds, thousands, and so on.

Exercise 1.1

What numbers are represented by the following numerals?

a) 48,902

b) 367,518

Solution 1.1

a) In 48,902:

• 4 is in the ten thousands place; it represents 4 × 10,000 = 40,000.
• 8 is in the thousands place; it represents 8 × 1,000 = 8,000.
• 9 is in the hundreds place; it represents 9 × 100 = 900.
• 0 is in the tens place; it represents 0 × 10 = 0.
• 2 is in the ones place; it represents 2 × 1 = 2. Thus, 48,902 represents 40,000 + 8,000 + 900 + 2 and is read, “forty-eight thousand, nine hundred two.”

b) In 367,518:

• 3 is in the hundred thousands place; it represents 3 × 100,000 = 300,000.
• 6 is in the ten thousands place; it represents 6 × 10,000 = 60,000.
• 7 is in the thousands place; it represents 7 × 1,000 = 7,000.
• 5 is in the hundreds place; it represents 5 × 100 = 500.
• 1 is in the tens place; it represents 1 × 10 = 10.
• 8 is in the ones place; it represents 8 × 1 = 8.

Thus, 367,518 represents 300,000 + 60,000 + 7,000 + 500 + 10 + 8 and is read, “three hundred sixty-seven thousand, five hundred eighteen.”

Exercise 1.2

Write the word names for the following numerals:

a) 333,222,111

b) 43,598,567,104

c) 329,862,107

d) 4,444,444,444

e) 4,832,367,756,523

Solution 1.2

a) The word name for the numeral 333,222,111 is three hundred thirty-three million, two hundred tw...