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THE MEANING OF DECIMALS Lesson 2 Section 3 In the Prologue, Elementary Addition, we introduced the number 0. We continue with the following question: 



This number 2001 is obviously very different from this number: 21. Those 0's signify No tens and No hundreds. Those units are absent from the expanded sum. 2001 = 2 Thousands + 0 Hundreds + 0 Tens + 1 One. 



Consider the expanded forms:
The 0's add nothing to the value. Therefore a whole number, such as 8, could be written as 8.0 or 8.00 or 8.0000000 0's on the extreme right of a decimal Similarly, 0's on the left of a whole number do not change its value. 65 = 065 = 0000065 Example. Rewrite each number and eliminate the unnecessary 0's. a) 5.6000 = 5.6 b) 08 = 8 c) .08 This cannot be changed. 8 is in the hundredths place. d) 204.006 This cannot be changed either. We may not eliminate Comparing decimals 



Example 1. Which of these numbers is smallest, and which is largest? .34 .306 .2986 Answer. .2986 is the smallest number, and .34 is the largest. For, consider each digit in turn. .34 .306 .2986 With respect to the first decimal place, .2986 has only 2 tenths, while the others have 3. (Question 5.) 2 tenths is less than 3 tenths (and adding hundredths to it will not make it more). Therefore .2986 is the smallest number. As for .34 versus . 306 again, they are equal in the first decimal place. Therefore we will compare them in the second place. .34 has 4 hundredths, while .306 has 0 hundredths. 4 hundredths are more than 0 hundredths. Therefore, .34 is the largest number. Example 2. Which is the largest number? .02 .0201 .021 Answer. .021 .02 .0201 .021 For, these numbers are equal in the first two decimal places; each has .02. Therefore we must look at the third place. .02 effectively has a 0 in the third place. The next number .0201 also has 0 in the third place. But .021 has 1 in the third place. 1 is more than 0. Therefore, .021 is the largest number. Please "turn" the page and do some Problems. or Introduction  Home  Table of Contents Please make a donation to keep TheMathPage online. Copyright © 20012007 Lawrence Spector Questions or comments? Email: themathpage@nyc.rr.com 