Associated Topics || Dr. Math Home || Search Dr. Math

### Multiplying by a Decimal Number

```
Date: 02/28/2001 at 14:34:14
From: Carolyn Trancovich
Subject: Multiplication of decimal numbers

I am having trouble understanding why multiplying by decimal numbers
gives a product smaller than the factors. For example, 5 * .43 = 2.15.
I just always thought that multiplying would make the product bigger
than the numbers I used.

Thank you.
```

```
Date: 02/28/2001 at 16:49:42
From: Doctor Rick
Subject: Re: Multiplication of decimal numbers

Hi, Carolyn.

When you only knew about whole numbers, you could make a rule like the
one you stated - but not quite! Even when you only knew about whole
numbers, there was one exception to your rule: multiplying by 1 does
not make a number bigger. When you added zero, that was another
exception.

If you multiply by a number greater than 1, the product will be
greater than what you started with. If you multiply by 1, the product
is the same as what you started with. If you multiply by a number less
than 1, the product is less than what you started with.

Let's make some sense of this by considering a simple example.

Multiplying by 1/2 is the same as dividing by 2. Do you understand
this? Multiplying by 1/2 means taking half of it; dividing by 2 means
cutting it in two pieces and keeping one. These amount to the same
thing. Since 1/2 = 0.5, and half of something is less than the whole,
it makes sense that multiplying a number by 0.5 makes it smaller.

You've asked a good question, and others have wondered about it, too.
Here are some answers I have written to other students on this topic:

http://mathforum.org/dr.math/problems/graham12.2.98.html

Multiplying by 1
http://mathforum.org/dr.math/problems/abbasi9.1.98.html

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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search