Powers of Ten

I was listening to my Schoolhouse Rocks CDs yesterday, and heard "My Hero, Zero" again for the first time in a long time. Most of us learned in school that if you put a zero after a number, you've multiplied it by 10. And if you take a zero away, then you've divided the number by 10.

This is what leads us to scientific notation. 10⁴ means 10 times itself 4 times, or 10 x 10 x 10 x 10. Well the easy way to do that is just to write a 1 followed by 4 zeros, 10000.
10¹ = 10
10² = 100
10³ = 1,000
10⁴ = 10,000
10⁵ = 100,000

So 2 x 10⁴ means that you take 10 ⁴ and then multiply it by 2, or 2 followed by 4 zeros (20,000).
7 x 10⁴ = 70,000
4 x 10⁴ = 40,000
6 x 10³ = 6,000
3 x 10² = 300
8 x 10⁵ = 800,000

And if that superscript number is negative, you're talking about fractions. 2 x 10^-4 is 1/20000.

Okay, so you can do scientific notation, but what does it all MEAN? I can tell you that a human blood cell is 8 x 10 ^-6 meters small, but you probably don't really understand how small that is. Or I can say that the Sun is 1.5 x 10¹¹ meters away, but you probably don't get how big that is. So here is a great video that shows you exactly what all of those numbers mean.

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