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Rough Draft

Here are some random additional examples of exponential notation.

Whats a 1000 divided by 10?
1,000. / 10. =
10³ / 10¹ =
10^{3 - 1} =
10² =
100.

Whats a million times a billion? (Here is a list.)
Well, a million is 1,000,000.
So a million times a billion is 1,000,000. × 1,000,000,000. =
10⁶ × 10⁹ =
10^{6 + 9} =
10¹⁵ =
Oh my, a 1. with 15 zeros, err...
1,000,000,000,000,000.

4,000,000,000 / 100 ?
(4. × 10⁹) / (1. × 10²) =
(4. / 1.) × 10⁹) / (1. × 10²) =
What is 100. × 1,000.?
(1. × 10²) × (1. × 10³)
Here is what makes it easier: 10^a × 10^b = 10 ^{a + b} !
(Dividing is similar, 10^a / 10^b = 10 ^{a - b} )
So... 10² × 10³ = 10 ^{2 + 3} = 10⁵, and
100. × 1,000. =
(1. × 10²) × (1. × 10³) =
(1. × 1.) × 10⁵ = 1. × 10⁵
= 100,000.

Sorry, I've made this difficult.
Since 100. is 1. × 10², you would really just say 100 = 10².
So 100 × 1000 = 10² × 10³ = 10^{2 + 3} = 10⁵ = 100,000.
I mixed in the 1.'s so you could do things like 600 × 4000.
(6. × 10²) × (4. × 10³) = (6. × 4.) × 10^{2 + 3} = 24. × 10⁵ = 2,400,000.
You could even divide them. Whats 600 / 4000?
(6. × 10²) / (4. × 10³) = (6. / 4.) × 10^{2 - 3} = 3/2 × 10^-1 =
1.5 × 10^-1 = .15
(Though we usually write 0.15 to make sure noone overlooks the decimal.)

Overhaul or punt. Seems of little value as is.