A student was working on this problem the other day:

Find the volume of a cone with radius 2.5 units and height 5 units.

Of course we *all* remember the formula as

$latex V = \frac{1}{3} \pi \times r^2 \times h$

So she plugged in her numbers and got 29.45 cubic units. She checked the back of the book and was disappointed to see the answer listed as 32.72 cubic units.

Turns out she was using 0.3 instead of 1/3!

### What’s wrong with the answer?

I asked her to calculate with 0.33 instead. She got 32.39 – far closer to the answer from the book.

Then I asked her to use 0.333. This yielded 32.69. She was amazed at how adding another 3 got her closer to the answer.

Using four decimal places of 3’s finally got her there.

She was happy with that. Then she asked, “But what is the difference between 0.3 and 0.33?”

### What IS the difference between 0.3 and 0.33?

I had previously reminded her how to divide fractions to get the decimal approximation. Which is how she confidently came up with 0.3.

Traditionally we show students that 0.3 is the same as 0.30. Then comparing 0.30 with 0.33 is supposed to give them the aha moment.

Supposed to.

I’d been working with hundreds charts in another class so I broke out a couple of those and some crayons.

After 90 seconds I was able to show her visually the difference.

### Now how about 0.333…

I’m itching to make a Thousands Chart now to see how I can visually show 0.33 vs. 0.333. But that might have to wait… 😀

What’s your favorite way to show these differences? Share in the comments.

**And ask others on Twitter, Facebook and Pinterest!**

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Hey super woman! You totally rock. Thanks for spending some quality (aka exercising) time with me. I find you super smart and I love your personality. I’ll be following your social media platforms and I hope to run with you at Houston if not before. {hugs}

Cintia

Thanks! I had a great time too.

Perhaps there’s a math and marathons post in my future (wanna guest post on that?).