1. Scientific notation is a quick way of writing very large or very small numbers. Scientific Notation & Significant Digits Example #1 Write 234 000 000 m/s in scientific notation. 2.34 x 10 8 m/s. The decimal is moved until there is only one non-zero digit to the left. To show that the decimal has moved 8 places to the left, a positive exponent of 8 has been given to the base 10.

2. Example #2 Write 0.000 000 000 478 s in scientific notation. 4.78 x 10 -10 s. The decimal has been moved 10 places to the right. A negative exponent of 10 has been given to the base.

3. Significant Digits In any given number, some digits are significant, and some are not. To decide which digits are which a set of rules must be followed. All non-zero digits are significant. (ie. 374 has three significant digits) All leading zeros are not significant. (ie. 0.000 035 has 2 significant digits). If there is no decimal point, all trailing zeros are not significant. (ie 125 000 has three significant digits).

4. All digits used in the coefficient of a number written in Scientific notation are significant. (ie. 3.500 x 10 3 has 4 significant digits). smallest The number of significant digits in the answer to a problem should always equal the smallest number of significant digits in the given data.

5. Example #3 State the number of significant digits in each of the following. a) 564b) 2500c) 3.0 d) 1.350e) 0.005f) 2.00 x 10 2 g) 250 001h) 0.34i) 0.00 304 0

6. Example #4 Round each of the following to 3 significant digits. a)2.375b) 6.7c) 5 d) 2e) 20f) 200