Chapter 14

A Perfect Ten: Condensing Numbers with Scientific Notation

In This Chapter

arrow Knowing how to express powers of ten in exponential form

arrow Appreciating how and why scientific notation works

arrow Understanding order of magnitude

arrow Multiplying numbers in scientific notation

Scientists often work with very small or very large measurements — the distance to the next galaxy, the size of an atom, the mass of the Earth, or the number of bacteria cells growing in last week's leftover Chinese takeout. To save on time and space — and to make calculations easier — people developed a sort of shorthand called scientific notation.

Scientific notation uses a sequence of numbers known as the powers of ten, which I introduce in Chapter 2:

  • 1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 ...

Each number in the sequence is 10 times more than the preceding number.

Powers of ten are easy to work with, especially when you're multiplying and dividing, because you can just add or drop zeros or move the decimal point. They're also easy to represent in exponential form (as I show you in Chapter 4):

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