7: Division

Detour: Multiplying and Dividing Scientifically

Somewhere along the line, you probably learned the “rule of 10” — to multiply two numbers
that are followed by zeros, you need to multiply the numbers (without zeros) then add the total
number of zeros, like this:

7000 x 800 = 7 x 8 (plus 5 zeros) = 5,600,000

Well, scientific notation works EXACTLY the same:

7 × 10³ x 8 × 10² = 7 x 8 (plus 5 zeros) = 56 × 10⁵

In shorthand: multiply the numbers, add the zeros.

Division is similar — divide the numbers, subtract the zeros:

5,600,000 / 7000 … cancel 3 zeros …
5600/7 = 800

56 × 10⁵ / 7 × 10³ = 56/7 (with (5-3) zeros) = 8 × 10² .

…and…