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Multiplication of Decimals

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Date: 01/02/2002 at 11:03:43
From: Emma
Subject: Multiplication of Decimals

Find the value of 36.5 x 3.504.

I ignored the decimals and worked out the answer and discovered that
when the numbers after the decimals are added together, the decimal
point can then be placed that number of places from the right.

For example, the total number of decimal places moved for the sum
above is four, and I know the answer is 1278960 and when the decimal
point is placed the answer will be 127.8960. But I don't know why or

Many thanks.
```

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Date: 01/04/2002 at 02:31:38
From: Doctor Ann
Subject: Re: Multiplication of Decimals

Dear Emma,

Thank you for writing to Dr. Math. You have asked a good question. I
hope this explanation helps:

Let's re-write your problem:

36.5 x 3.504 = 365 x (.1) x 3504 x (.001)

(Do you agree with this?)

Now use the commutative law to rearrange to:

= 365 x 3504 x  (.1) x (.001)

= 1278960    x   (.0001)

(Do you recognize this?)

I hope that from this you can see why you can "ignore the decimals and
work out the problem" and then adjust the decimal point for the final

If you have another question, please feel free to write to Dr. Math.

- Doctor Ann, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Fractions

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