Section 5.1 & 5.3 A

1. Section 5.1 & 5.3 A Period 1 Group # 3

2. Scientific Notation Definition • Scientific Notation expresses a number as a product of a number between 1 through 10 and the appropriate power of 10.

3. Representing Large and Small Numbers • 62,000 = 6.2 x 104 , place a decimal at the right end and move 4 to the left. • .0021 = 2.1 x 10-3, move the decimal 3 times to the right, and add a -3 exponent on the 10.

4. Example: Scientific Notation • Solve each of the following. Which of the two measurements is greater? • A) 2.67 x 104 • B) 287.2 x 10-2

5. Answer: Scientific Notation • A) 26700 • B) 2.872 • Answer: A is greater.

6. Remember! • Moving the decimal point to the left requires a positive exponent. • Moving the decimal point requires a negative exponent. • Any # can represent the product of numbers between 1-10. • The power of 10 depends on number of decimal places moved.

7. Units Definition • Unit: The part of a measurement telling us the scale being used. Think about these questions. • Why are units important? • Why are units needed? • How are units represented? (results from a measurement)

8. Metric and English System • Metric system is used by most of the industrialized world. • The English system is used by the United States.

9. International System (SI) • International system (SI) is based on the metric system. • Most common units are gram, meter, and liters.

10. Example: Units • Are units quantitative or qualitative part of a measurement? Explain.

11. Answer: Units • Units are quantitative part of a measurement, because they deal with numbers.

12. Common Prefixes • Common Prefixes are mili, centi, deci, kilo, etc.

13. Measurements of Length, Mass, and Volume • Length = the longest extent from end to end. • Mass = Quantity of matter present in an object. • Volume = Amount of a three-dimensional space occupied by a substance. (Whenever dealing with volume, always cube the units). • Example: m3

14. Examples of Commonly Used Units • Commonly used units are milliliters, liters, grams, inches, and centimeters.

15. Questions we Ask Ourselves to Solve a Problem • Questions we can ask ourselves when solving a problem. • Where do we want to go? • What do we know? • How do we get there? • Does it make sense?

16. Example: Tools for Problem Solving • How does asking yourself questions such as “What do we know?” and “Where do we want to go?” help you solve problems?

17. Answer: Tools for Problem Solving • When you ask these questions to yourself, you get a better overview and understanding of the problem. (Answers may vary).

18. Conversion Factor Definition • Conversion Factor is the ratio of the two parts of the statement that relates two units.

19. Equivalence Statement • Equivalence Statement: equivalent measures from the English and Metric Systems. • Example: 2.54 cm = 1 inch

20. Example: Choosing Conversion Factors • A caretaker of the aquarium needs to find the dimensions of a tank. The height is 10 feet, the width is 4 yards, and the length is 96 inches. Wherefore, her dimensions were 10 x 4 x 96. Explain the error.

21. Answer: Choosing Conversion Factors • Answer: 120 x 144 x 96 • You have to convert all the units to satisfy the problem. • Convert all units to inches. • 10 feet = 120 inches, 4 yards = 12 feet = 144 inches, and 96 inches.

22. Quiz Time! • A) Is the following conversion to scientific notation correct? If not correct the scientific notation. --0.00217 -> 21.7 x 104 • B) Why are prefixes such as mega, kilo, deci, centi, and mili needed? • C) Make the indicated conversions. -A) 17.0 L to milliliters -B) 8.25 to inches -C) 4.21 inches to centimeters • D) What are some questions you go through your mind as you are confronted with a problem? • E) Which conversion factor should be used to solve the problem? -7.62 cm x 2.54cm/1inch or 1in/2.54 = ? Inches.

23. Answers to Quiz! • A) 0.00217 -> 2.17 x 10-3 • B) Prefixes are needed, because then you know the quantity of a unit. It also makes an easier time writing all the zeroes. • C) a) 1700 milliliters b) 324.8 inches c) 10.7 centimeters • D) “Why is this problem so hard?” Answers may vary. • E) You should of chose 1 inch/ 2.54 centimeters.

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