What I was going to go over tonight was percentages.

There's almost an "optical illusion" in the way percentages transfer to decimals. It's easy enough to see that
**0.75 is 75%**, and that **23% would be 0.23** as a decimal. (I like to use the "leading zero" in my decimals, your student should check with her teacher, (or employer!) to make sure she keeps up with accepted standards and practices.)

The use of zero is where it starts to get tricky. For example, **20%** could be stated as just
**0.2** and be correct, without showing its heritage as **0.20**. However, this sometimes leads one to think that
**7%** can be **0.7** instead of 7/100 which is **0.07**.

We have to imagine a "**leading zero**" on single digit percents, as if we were changing something like "**07%**" to
**0.07** decimal. Ask your student about "ghost numbers" we have talked about. This could be added to that list as another example.

Another optical illusion is in our checkbooks these days. Okay, add your own punchline to that, but you and I had been used to getting
**3%** interest on savings, which would be decimal **0.03** in accordance with what we just said above. However, Annual Percentage Rates (APR) we're getting now are
**0.03%** which at first blush LOOKS like it should be the same as what we are used to (prior to 2008) but it's really
**much** smaller, and works out as a 'decimated' decimal, that looks like this:
**0.0003** so the 'earned' interest that used to buy Mothers' Day Dinner out for four won't even pay a fourth of the tip now.

Another thing about percentages, since you can't calculate with them, it doesn't matter how mixed up they get. 3.75% is the same as 3 3/4 %, it just depends on which way the bank thinks will attract more mortgage re-finance customers. Maybe that seven looks a lot bigger than a three or a four, in print. I have a fraction to decimal practice sheet to familiarize your student with some more examples like that.

Gotta leave something for another blog.