Contemporary Mathematics for Business and Consumers Third Edition By: Robert A. Brechner Contemporary Mathematics for Business and Consumers Third Edition By: Robert A. Brechner COPYRIGHT © 2003 by South-Western, a division of Thomson Learning. Thomson Learning TM is a trademark used herein under license. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means–graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution or information storage and retrieval systems–without the written permission of the publisher. For permission to use material from this text or product, contact us by Tel (800) Fax (800)

Chapter 3 Decimals Copyright © 2003 by South-Western

SECTION I: Understanding Decimal Numbers 3-1 Reading and Writing decimal numbers in the numerical and word form 3-2 Rounding decimal numbers to a specified place value SECTION II: Decimal Numbers and the Fundamental Process 3-3 Adding and Subtracting decimals 3-4 Dividing decimals SECTION III: Conversion of Decimals to Fractions and Fractions to Decimals 3-6 Converting decimals to fractions 3-7 Converting fractions to decimals Chapter 3, Outline

Chapter 3, Section I Understanding Decimal Numbers 3-1 Reading and Writing Decimal Numbers in Numerical and Word Form

EVERYBODY’S BUSINESS When reading numbers, remember that decimals start with the “tenths place, whereas whole numbers start with the “ones” place. Don’t forget that the word “and “is used to represent the decimal.

3-2 Steps to Round Decimals to a Specified Place Value Step 1. Determine the place to which the decimal is to be rounded. Step 2a. If the digit to the right of the one being rounded is 5 or more, increase the digit in the place being rounded by 1. Step 2b. If the digit to the right of the one being rounded is 4 or less, do not change the digit in the place being rounded. Step 3. Delete all digits to the right of the one being rounded.

CHAPTER 3, SECTION II Decimal Numbers and the Fundamental Process

3-3 Adding and Subtracting Decimals Steps for Adding and Subtracting Decimals: Step 1. Line up all the place values and decimal points vertically. Step 2. (Optional) Add zeros to the right of the decimal numbers that do not have enough places. Step 3. Perform the addition or subtraction, working from right to left. Step 4. Place the decimal point in the answer in the same position (column) as in the problem.

3-4 Multiplying Decimals Steps for Multiplying Decimals: Step 1. Multiply the numbers as if they are whole numbers. Disregard the decimal points. Step 2. Total the numbers of decimal places in the multiplier and the multiplicand. Step 3. Insert the decimal point in the product, giving the same number of decimal places as the total from step 2. Step 4. If necessary, place zeros to the left of the product to provide correct number of digits.

3-5 Dividing Decimals Steps for Dividing Decimals if the Divisor is a Whole Number: Step 1. Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2. Divide the numbers.

3-5 Dividing Decimals Steps for dividing decimals if the divisor is a decimal number: Step 1. Move the decimal point in the divisor to the right until it becomes a whole number. Step 2. Move the decimal point in the dividend the same number of places as you moved it in the divisor. It may be necessary to add zeros to the right of the dividend if there are not enough places. Step 3. Place the decimal point in the quotient directly above the decimal point in the dividend. Step 4. Divide the numbers.

CHAPTER 3, SECTION III Conversion of Decimals to Fractions and Fractions to Decimals

3-6 Converting Decimals to Fractions Steps for converting decimals to their fractional equivalent: Step 1. Write the decimal as a faction by making the decimal number, without the decimal point, the numerator. Step 2. The denominator is 1 followed by as many zeros as there are decimal places in the original decimal number. Step 3. Reduce the fraction to lowest terms.

3-7 Converting Fractions to Decimals Steps for Converting Fractions to Decimals: Step 1. Divide the numerator by the denominator. Step 2. Add a decimal point and zeros, as necessary, to the numerator (dividend).

CHAPTER 3 Decimal numbers, or decimals: Amounts less than whole numbers, or less than one. For example,.44 is a decimal. Decimal Point: A dot written in a decimal number to indicate where the place values change from whole numbers to decimal numbers. Mixed decimals: Decimals written in conjunction with whole numbers. For example, 2.44 is a mixed number.