Proper way to write this math

1. Dec 27, 2011

lenfromkits

I have a situation where I have two formulas that relate together but do not really transition from one to the other and I'm not sure how to properly write this as a single formula.

I have these two cases:
$when \ b<100: a=b*4$

$when \ b>=100: a=\frac{b}{4}$

I just need a nicer more professional way of writing that as one formula.

Thanks.

2. Dec 28, 2011

JHamm

3. Dec 28, 2011

lenfromkits

Perfect. Thank you!!

4. Dec 28, 2011

HallsofIvy

Or, if you prefer it on one line,
$$a(b)= 4b+ \left(\frac{4}{b}- 4b\right)H(b- 100)$$
where H(x) is the "Heviside step function" which is 0 for x< 0, 1 for $x\ge 0$.

5. Dec 28, 2011

JHamm

You math kids, and just as I was feeling clever too...