Fraction or Decimal Form?

Date: 07/30/2002 at 16:47:20
From: Joe
Subject: Algebra - fraction form or decimal form?

Hi,

I've been learning Algebra for a while now and am enjoying it. I'm 
just wondering, is it correct to use fraction forms or decimal forms? 
I'll give an example:

  1/2{6x - 3(2x - 1)}  

I believe could also be expressed as:

  0.5{6x - 3(2x - 1)}

And when all is said and done (or more conventionally you could say 
'after simplification') the result could be expressed as either 3/2 
or 1.5.

The workbook I've been working from always gives the answers in 
fractional form. The trouble is, I'm more confident with decimals than 
I am with fractions. Which is the right way?

Thank you.

Date: 07/30/2002 at 17:44:24
From: Doctor Ian
Subject: Re: Algebra - fraction form or decimal form?

Hi Joe,

In the examples you've used, the answers are exactly equivalent, so 
either is fine. Where you have to be careful is when you truncate 
fractions like 3/7 to 0.429 instead of the more exact
    ______
  0.428571

This is one reason that mathematicians tend to prefer the fractional 
form: it's exact.

A second reason is that when you leave things in fractional form, it's 
easier to spot opportunities for terms to cancel each other out. For 
example, in

  (3/8)(64x^2 - 16x)

it's obvious that the (1/8) can be distributed to get

  3(8x^2 - 2x)

whereas it's less obvious when written as 

  0.375(64x^2 - 16x).

But as long as you're careful to distinguish between exact and 
approximate decimal representations, feel free to use whichever one 
you like best. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 07/31/2002 at 10:50:15
From: Joe
Subject: Algebra - fraction form or decimal form?

Hi again. Thanks for the feedback. I see that it's better to use 
fractions because it's important to cancel down. I'll just have to 
get used to it.