### Scientific Notation

Very large and very small numbers are cumbersome.

EXAMPLE:

one option: 600,000,000s = 600 Ms

another: 600,000,000s = 6x10^{8}s

Either option (compound units or scientific notation) works for
both large and small

(0.000001m = 1 micrometer = 1x10^{-6}m)

OUTCOME:

Write a value in scientific notation (using the
correct number of significant digits)

TEST YOURSELF!

Write the number of seconds in a day using
scientific notation.

Why use scientific notation?

### Significant Figures

Represent the precision at which a value is known.

EXAMPLE:

Clock without a second hand -> 10:21
AM

Clock with a second hand -> 10:21:08 AM

Stop watch -> 10:21:08.12 AM

Writing numbers to show sig. figs.

- with decimal: count from non-zero on left to last digit on
right
- without decimal: count from non-zero on left to last non-zero
on right
- scientific notation: typically only sig. figs. are shown

EXAMPLE:

40500 (4.05x10^{4}) -> 3 sig.
figs.

40500. (4.0500x10^{4}) -> 5 sig. figs.

0.0012 (1.2x10^{-3}) -> 2 sig. figs.

0.001200 (1.200x10^{-3}) -> 4 sig. figs.