Copyright © Cengage Learning. All rights reserved. Functions 1 Basic Concepts

Copyright © Cengage Learning. All rights reserved. Unit 1C Review of Operations with Decimal Fractions and Percent

Copyright © Cengage Learning. All rights reserved. Rounding Numbers 1.11

4 Rounding Numbers We often need to make an estimate of a number or a measurement. When a truck driver makes a delivery from one side of a city to another, he or she can only estimate the time it will take to make the trip. An automobile technician must estimate the cost of a repair job and the number of mechanics to assign to that job. On such occasions, estimates are rounded.

5 Rounding Numbers Earlier, you found that There is no exact decimal value to use in a calculation. You must round to a certain number of decimal places, depending on the accuracy needed in a given situation.

6 Example 1 Round 25,348 to the nearest thousand. Note that 25,348 is more than 25,000 and less than 26,000.

7 Rounding Numbers Note: If a number is exactly halfway between two numbers, round up to the larger number. Rounding Numbers to a Particular Place Value To round a number to a particular place value: 1. If the digit in the next place to the right is less than 5, drop that digit and all other following digits. Use zeros to replace any whole-number places dropped. 2. If the digit in the next place to the right is 5 or greater, add 1 to the digit in the place to which you are rounding. Drop all other following digits. Use zeros to replace any whole-number places dropped.

8 Example 3 Round each number in the left column to the place indicated in each of the other columns.

9 Rounding Numbers Instead of rounding a number to a particular place value, we often need to round a number to a given number of significant digits. Significant digits are those digits in a number we are reasonably sure of being able to rely on in a measurement.

10 Rounding Numbers Here we present a brief introduction to significant digits. Significant Digits The following digits in a number are significant: All nonzero digits (258 has three significant digits) All zeros between significant digits (2007 has four significant digits) All zeros at the end of a decimal number (2.000 and have four significant digits)

11 Rounding Numbers The following digits in a number are not significant: All zeros at the beginning of a decimal number less than 1 ( has three significant digits) All zeros at the end of a whole number (36,000 has two significant digits)

12 Rounding Numbers Rounding Numbers to a Given Number of Significant Digits To round a number to a given number of significant digits: 1. Count the given number of significant digits from left to right, starting with the first nonzero digit. 2. If the next digit to the right is less than 5, drop that digit and all other following digits. Use zeros to replace any whole-number places dropped.

13 Rounding Numbers 3. If the next digit to the right is 5 or greater, add 1 to the digit in the place to which you are rounding. Drop all other following digits. Use zeros to replace any whole-number places dropped.

14 Example 4 Round each number to three significant digits. a. 74,123 b Count three digits from left to right, which is the digit 1. Since the next digit to its right is less than 5, replace the next two digits with zeros. Thus, 74,123 rounded to three significant digits is 74,100. Count three nonzero digits from left to right, which is the digit 7. Since the next digit to its right is greater than 5, increase the digit 7 by 1 and drop the next four digits. Thus, rounded to three significant digits is