# 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...