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Significant Figures and Scientific NotationPowerPoint Presentation

Significant Figures and Scientific Notation

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### Significant Figures and Scientific Notation

Precision in measurement

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. 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.

- 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

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.

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.

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.

- 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

- Numbers following exponent rules.

- (7.21 x104 )+ (2.4 x 103)

- (7.41 x 105cm) x (8.2 x 102cm)

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