Decimal Numerators & Denominators

Explain this!

New member
Joined
Feb 7, 2019
Messages
10
Why are decimals not used as numerators and denominators?

For example, 0.4% can be expressed as (4/10)/100 as complex fraction, but 0.4/100 with a decimal numerator is not common.
The same with 100/(4/10) but not 100/0.4.
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,784
Why are decimals not used as numerators and denominators?

For example, 0.4% can be expressed as (4/10)/100 as complex fraction, but 0.4/100 with a decimal numerator is not common.
The same with 100/(4/10) but not 100/0.4.
Why not?

Convention, more than anything.
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,235
Why are decimals not used as numerators and denominators?

For example, 0.4% can be expressed as (4/10)/100 as complex fraction, but 0.4/100 with a decimal numerator is not common.
The same with 100/(4/10) but not 100/0.4.
The reason is that any rational number can be expressed as a fraction of whole numbers. Any terminating decimal is a rational number. So the obvious way to represent 0.4% in fractional form is 4/1000.

If you want to rerpesent a decimal by a fraction, why put decimals in the fraction.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,039
Why are decimals not used as numerators and denominators?

For example, 0.4% can be expressed as (4/10)/100 as complex fraction, but 0.4/100 with a decimal numerator is not common.
The same with 100/(4/10) but not 100/0.4.
I'd say the answer is very simple. We can use anything we want in a fraction while we are working (as you've shown); but in a final answer, we want the simplest possible form, and clearly mixing decimals into fractions is not simple. So we tend to avoid that.
 

Otis

Senior Member
Joined
Apr 22, 2015
Messages
1,170
Why are decimals not used as numerators and denominators? …
Decimal expressions appear in ratios regularly, at arithmetic class. :)

For example, we see exercises like the following.


Simplify the mixed number: \(\displaystyle 5\frac{0.\overline{6}}{9}\)


Express as a mixed number: \(\displaystyle \dfrac{\frac{4}{5}}{0.75}\)


Outside of arithmetic class, we don't see decimals written in ratios very often because that's not standard form.
 

Explain this!

New member
Joined
Feb 7, 2019
Messages
10
I'd say the answer is very simple. We can use anything we want in a fraction while we are working (as you've shown); but in a final answer, we want the simplest possible form, and clearly mixing decimals into fractions is not simple. So we tend to avoid that.

Yes, 4/1000 is easier to interrupt or understand than something like 0.4/100 or (4/10)/100, or perhaps even 0.4%, although are a lot of decimal percentages are used in business and finance.
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,235
Yes, 4/1000 is easier to interrupt or understand than something like 0.4/100 or (4/10)/100, or perhaps even 0.4%, although are a lot of decimal percentages are used in business and finance.
Yes, numbers like 0.4% or 40 basis points do come up a lot in presentations concerning business and finance.

What does not come up in such presentations are things like

\(\displaystyle \dfrac{4\%}{10}.\)
 
Top