Significant Figures

1. Significant Figures Indicate precision of a measured value 1100 vs. 1100.0 Which is more precise? How can you tell? How precise is each number? Determining significant figures can be tricky. There are some very basic rules you need to know. Most importantly, you need to practice!

2. Counting Significant Figures

3. Calculating With Sig Figs

4. Scientific Notation Number expressed as: Product of a number between 1 and 10 AND a power of 10 5.63 x 104, meaning 5.63 x 10 x 10 x 10 x 10 or 5.63 x 10,000 ALWAYS has only ONE nonzero digit to the left of the decimal point ONLY significant numbers are used in the first number First number can be positive or negative Power of 10 can be positive or negative

5. When to Use Scientific Notation Astronomically Large Numbers mass of planets, distance between stars Infinitesimally Small Numbers size of atoms, protons, electrons A number with “ambiguous” zeros 59,000 HOW PRECISE IS IT?

6. Powers of 10 Positive Exponents Exponent of Zero Means “1” 100 = 1

7. Powers of 10 Negative Exponents Exponent of Zero Means “1” 100 = 1

8. Converting From Standard to Scientific Notation Move decimal until it is behind the first sig fig Power of 10 is the # of spaces the decimal moved Decimal moves to the left, the exponent is positive Decimal moves to the right, the exponent is negative 428.5  4.285 x 102(decimal moves 2 spots left) 0.0004285  4.285 x 10-4(decimal moves 4 spots right)

9. Converting From Scientific to Standard Notation Move decimal point # of spaces the decimal moves is the power of 10 If exponent is positive, move decimal to the right If exponent is negative, move decimal to the left 4.285 x 102  428.5(move decimal 2 spots right) 4.285 x 10-4  0.0004285(decimal moves 4 spots left)