Significant Figures and Scientific Notation

1. Significant Figures and Scientific Notation Precision in measurement

2. Significant Figures • The number of digits that have meaning to precision of data • Rules • 1. All non-zero numbers ARE significant. The number 33.2 has THREE significant figures • 2. Zeros between two non-zero digits ARE significant. 2051 has FOUR significant figures. The zero is between a 2 and a 5.

3. 3. Leading zeros are NOT significant. They're nothing more than "place holders." The number 0.54 has only TWO significant figures. 0.0032 also has TWO significant figures. • 4. Trailing zeros to the right of the decimal ARE significant. There are FOUR significant figures in 92.00.

4. 5. Trailing zeros in a whole number with the decimal shown ARE significant. For example, "540." indicates that the trailing zero IS significant; there are THREE significant figures in this value. • 6. Trailing zeros in a whole number with no decimal shown are NOT significant. Writing just "540" indicates that the zero is NOT significant

5. For Example… • 123,000,000 has 3 significant figures. • Trailing 0’s are not significant. • 123,000,100 has 7 significant figures. • 0’s stuck in between other digits are significant. • 0.003604 has 4 significant figures.

6. Scientific Notation • Method of abbreviating very large or very small numbers. • Based on powers of 10. • 123,000,000 is expressed as 1.23 x 108 • This is because 108 would move the decimal 8 spots to the right.

7. Scientific Notation • 123,000,100 is expressed as 1.23001 x 108 • 0.003604 is expressed as 3.604 x 10-3 • This is because 10-3 would move the decimal place 3 spaces to the left.

8. Adding and Subtracting numbers in scientific notation. • Numbers should be rearranged such that exponents are the same. • Multiplying and Dividing numbers in scientific notation • Numbers following exponent rules. • Multiplying  Add exponents • Dividing  Subtract exponents

9. (7.21 x104 )+ (2.4 x 103)

11. (7.41 x 105cm) x (8.2 x 102cm)