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Zeros after the Decimal Point

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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.
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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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Associated Topics:
Elementary Fractions
Elementary Place Value

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