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Lesson 3 Section 3 THE FUNCTION OF 0COMPARING DECIMALSIn 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. The expanded form of 2001 is 2 Thousands + 0 Hundreds + 0 Tens + 1 One. The expanded form of 21 is 2 Tens + 1 One. Trailing and leading 0's




Consider these 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 do not change its value. Those 0's are called trailing 0's. They are 0's followed by no other digits. Similarly, 0's on the left of a whole number do not change its value. 65 = 065 = 0000065 Those are called leading 0's. Example 1. Rewrite each number and eliminate the unnecessary 0's. a) 5.6000 = 5.6 b) 006 = 6 c) 600.000 = 600 d) .06 This cannot be changed. 6 is in the hundredths place. e) 204.006 This cannot be changed either. We may not eliminate Comparing decimals




Example 2. 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 digit, .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, the first decimal digits are equal. Therefore we will compare the second digits. .34 has 4 hundredths, while .306 has 0 hundredths. 4 hundredths are more than 0 hundredths. Therefore, .34 is the largest number. Example 3. Which is the largest number? .02 .0201 .021 Answer. .021 .02 .0201 .021 For, the first two decimal digits are equal: .02. Therefore we must look at the third digit. .02 effectively has 0 as the third digit. The next number .0201 also has 0 as the third digit. But .021 has 1 as the third digit. 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 Copyright © 2021 Lawrence Spector Questions or comments? Email: themathpage@yandex.com 