Zeros after the Decimal Point
Date: 09/17/2001 at 22:19:53 From: Carolyn Bronk Subject: Decimals I have a group of students that just can't comprehend my explanation of how 3.70 is equivalent to 3.7 or 3.700 or 3.7000... especially when you say 3.70 is 3 and 70 hundredths. Can you give me some insight into how you might go about the process of explaining the equivalent aspect of this concept? Thanks. P.S. I have noted that adding the extra zeros does not change the value.
Date: 09/18/2001 at 08:59:47 From: Doctor Peterson Subject: Re: Decimals Hi, Carolyn. There are two main ways to explain this: By place value: 3.7 = 3(1) + 7(1/10) 3.70 = 3(1) + 7(1/10) + 0(1/100) The only difference between them is adding an expression that is equal to zero. This differs from the case for whole numbers, where adding a zero on the right changes the place value of all the other digits (e.g. 37 -> 370); but it is the same as adding a zero on the LEFT of a whole number (37 -> 037), where nothing is changed. By equivalent fractions: 3.7 = 3 7/10 3.70 = 3 70/100 The fractional parts are equivalent, because the latter can be obtained from the former by multiplying numerator and denominator by 10: 7 7 * 10 70 --- = ------- = --- 10 10 * 10 100 When we add a zero on the end, we are multiplying both the numerator and the denominator by 10, so the value doesn't change. I don't know whether this helps. If you still face resistance, you might want to make it more concrete (say, ask whether they want you to give them three dollars and seventy cents, or three dollars and seven dimes). Or, ask them to convince you that the numbers are different, and then tell me what they said so I can see their reasoning. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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