# EC: Write a value in scientific notation

### Scientific Notation

Very large and very small numbers are cumbersome.

EXAMPLE:

one option: 600,000,000s = 600 Ms
another: 600,000,000s = 6x108s

Either option (compound units or scientific notation) works for both large and small
(0.000001m = 1 micrometer = 1x10-6m)

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 (4.05x104) -> 3 sig. figs.
40500. (4.0500x104) -> 5 sig. figs.
0.0012 (1.2x10-3) -> 2 sig. figs.
0.001200 (1.200x10-3) -> 4 sig. figs.