# Decimal Numerators & Denominators

#### Explain this!

##### New member
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
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
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
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
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
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
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

$$\displaystyle \dfrac{4\%}{10}.$$