# Decimal powers

• September 15th 2012, 07:36 AM
ineedmathshelp
Decimal powers
just curious to know if its ok to write powers of a number as decimals or if they have to be fractions in order to be marked as correct in an exam.

e.g. a^1/2 * a^2

is it correct to write the answer as a^2.5 or does it have to be a^5/2 in an exam.

(the answer in the back of the book was a^5/2 but id like to know if it would still be marked correct in an exam if you wrote it as a^2.5)
• September 15th 2012, 07:39 AM
MaxJasper
Re: Decimal powers
5/2 looks like an exact number while 2.5 leaves doubts of whether it is truncated or not....so on....
• September 15th 2012, 07:40 AM
a tutor
Re: Decimal powers
5/2 = 2.5 so there's no problem. However fractions are often easier to work with.
• September 15th 2012, 08:11 AM
Soroban
Re: Decimal powers
Hello, ineedmathshelp!

What would you do with $\sqrt[3]{x}$ ?

The correct form is: . $x^{\frac{1}{3}}$

Would you write it as $x^{0.3}$ or $x^{0.33}$ or $x^{0.333}$ ?

Consider: $\sqrt[3]{8}$

The cube root of 8 is 2 . . . right?

$\text{But: }\:\begin{Bmatrix}8^{0.3} &=& 1.8661... \\ 8^{0.33} &=& 1.9862... \\ 8^{0.333} &=& 1.9986... \\ \vdots && \vdots \end{Bmatrix} \quad\text{None of these is correct.}$

• September 15th 2012, 08:32 AM
SworD
Re: Decimal powers
Yes but Soroban, $4^{0.5} = 2$ IS correct. So how can we be sure you HAVE to use fractions even when the exact decimal is available? I don't really know how to answer this, I'd say it depends on the professor/teacher, but maybe there's some kind of notation rule that I'm not aware of or something... Maybe you should use fractions to be safe.
• September 15th 2012, 08:56 PM
Prove It
Re: Decimal powers
Quote:

Originally Posted by SworD
Yes but Soroban, $4^{0.5} = 2$ IS correct. So how can we be sure you HAVE to use fractions even when the exact decimal is available? I don't really know how to answer this, I'd say it depends on the professor/teacher, but maybe there's some kind of notation rule that I'm not aware of or something... Maybe you should use fractions to be safe.

I agree, if you use fractions you can't go wrong.