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# 1-3 Scientific Notation

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### 1-3 Scientific Notation

1. 1. Warm-up <ul><li>Which number is the largest? </li></ul><ul><li>a. 1.13 x 10 9 b. 3.51 x 10 3 c. 5.88 x 10 5 d. 7.92 x 10 2 </li></ul><ul><li>Which unit can be used to measure volume? </li></ul><ul><li>a. m b. m 2 c. m 3 </li></ul><ul><li>Which of the following units is the longest? </li></ul><ul><li>a. meter b. centimeter c. kilometer d. millimeter </li></ul>
2. 2. 1-3 Scientific Notation <ul><li>Perform calculations involving scientific notation. </li></ul><ul><li>Determine significant figures. </li></ul>
3. 4. Law vs. Theory <ul><li>Law – a rule of nature </li></ul><ul><li>Answers the question “what?” </li></ul><ul><li>Examples: Law of Attraction and Repulsion, Law of Universal Gravitation </li></ul><ul><li>Theory – An explanation based on repeated experimentation and observation. </li></ul><ul><li>Answers the question “why” </li></ul><ul><li>Examples: Theory of Evolution, Atomic Theory </li></ul>
4. 5. Law vs. Theory <ul><li>Theories do not become laws!!! What doesn’t replace why! </li></ul><ul><li>A theory represents everything currently known about a topic. </li></ul>
5. 6. Scientific Notation <ul><li>A number written as a product of two numbers: a coefficient and a power of 10 </li></ul><ul><li>Designed for the expression of very big and very small numbers </li></ul><ul><ul><li>3.6 x 10 4 </li></ul></ul><ul><ul><li>1 gram of hydrogen contains 301,000,000,000,000,000,000,000 molecules </li></ul></ul><ul><ul><li>3.01 x 10 23 molecules </li></ul></ul><ul><li>0.00081 = 8.1 x 10 -4 </li></ul><ul><ul><li>Decimal moves 4 place to the right </li></ul></ul><ul><li>34,000 = 3.4 x 10 4 </li></ul><ul><ul><li>Decimal move 4 places to the left </li></ul></ul>
6. 7. Significant Figures <ul><li>A method of expressing error in measurement. </li></ul><ul><li>Measure a value and then estimate one degree below the limit of the reading . </li></ul><ul><li>5.35 cm </li></ul>
7. 8. Significant Figures <ul><li>Atlantic – Pacific Rule </li></ul><ul><li>Pacific – &quot;P&quot; is for decimal point is present Count significant digits starting with the first non-zero digit from the left. </li></ul><ul><ul><li>0.004703 has 4 significant digits. </li></ul></ul><ul><ul><li>18.00 also has 4 significant digits. </li></ul></ul><ul><li>Atlantic – &quot;A&quot; is for decimal point is absent . Start counting significant digits with the first non-zero digit from the right. </li></ul><ul><ul><li>140,000 has 2 significant digits. </li></ul></ul><ul><ul><li>20060 has 4 significant digits. </li></ul></ul>
8. 9. Examples <ul><li>50.3 </li></ul><ul><ul><li>3 SF </li></ul></ul><ul><li>0.0008 </li></ul><ul><ul><li>1 SF </li></ul></ul><ul><li>200200 </li></ul><ul><ul><li>4 SF </li></ul></ul><ul><li>57.00 </li></ul><ul><ul><li>4 SF </li></ul></ul><ul><li>490 </li></ul><ul><ul><li>2 SF </li></ul></ul><ul><li>10000000 </li></ul><ul><ul><li>1 SF </li></ul></ul>
9. 10. 1-3 Summary <ul><li>What is scientific notation? </li></ul><ul><ul><li>Scientific notation is used to express very large or very small numbers. </li></ul></ul><ul><li>What are significant figures? </li></ul><ul><ul><li>Significant figures tell us how important the numbers are. </li></ul></ul>