Technical Mathematics, Sixth Edition

1.7. Scientific Notation and Engineering Notation

▪ Exploration:

Try this. On your calculator, multiply

500,000,000 × 300,000,000

What did your calculator show for this calculation? Can you explain the meaning of your display? Try multiplying some other very large or very small numbers and try to explain the display.

If our answers in the exploration have too many zeros for the display, the calculator will automatically switch into the kind of notation that we will study in this section. The display

1.5 E17

contains two parts: a decimal number, here 1.5, and an integer, 17. We read this as the decimal number times 10 raised to the value of the integer, or

1.5 × 10¹⁷

Here, 10¹⁷ is called a power of ten.

Your display might be different, partly depending on your settings.

1.7.1. Powers of 10

We did some work with powers in Sec. 1–5. We saw, for example, that 2³ meant

2³ = 2 • 2 • 2 = 8

Here, the power 3 tells how many 2's are to be multiplied to give the product. For powers of 10, the power tells how many 10's are to be multiplied to give the product.

Example 68: Here are some powers of ten expressed as decimal numbers. 102 = 10 × 10 = 100 103 = 10 × 10 × 10 = 1000

Example 69: Here are some demical numbers expressed as powers of ten. 10,000 = 104 1,000,000 = 106

We can evaluate ...