S ECTION 5.1 & 5.3 A Period 1 Group # 3

S CIENTIFIC N OTATION D EFINITION Scientific Notation expresses a number as a product of a number between 1 through 10 and the appropriate power of 10.

R EPRESENTING L ARGE AND S MALL N UMBERS 62,000 = 6.2 x 10 4, place a decimal at the right end and move 4 to the left = 2.1 x 10 -3, move the decimal 3 times to the right, and add a -3 exponent on the 10.

E XAMPLE : S CIENTIFIC N OTATION Solve each of the following. Which of the two measurements is greater? A) 2.67 x 10 4 B) x 10 -2

A NSWER : S CIENTIFIC N OTATION A) B) Answer: A is greater.

R EMEMBER ! 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 The power of 10 depends on number of decimal places moved.

U NITS D EFINITION 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)

M ETRIC AND E NGLISH S YSTEM Metric system is used by most of the industrialized world. The English system is used by the United States.

I NTERNATIONAL S YSTEM (SI) International system (SI) is based on the metric system. Most common units are gram, meter, and liters.

E XAMPLE : U NITS Are units quantitative or qualitative part of a measurement? Explain.

A NSWER : U NITS Units are quantitative part of a measurement, because they deal with numbers.

C OMMON P REFIXES Common Prefixes are mili, centi, deci, kilo, etc.

M EASUREMENTS OF L ENGTH, M ASS, AND V OLUME 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: m 3

E XAMPLES OF C OMMONLY U SED U NITS Commonly used units are milliliters, liters, grams, inches, and centimeters.

Q UESTIONS WE A SK O URSELVES TO S OLVE A P ROBLEM 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?

E XAMPLE : T OOLS FOR P ROBLEM S OLVING How does asking yourself questions such as “What do we know?” and “Where do we want to go?” help you solve problems?

A NSWER : T OOLS FOR P ROBLEM S OLVING When you ask these questions to yourself, you get a better overview and understanding of the problem. (Answers may vary).

C ONVERSION F ACTOR D EFINITION Conversion Factor is the ratio of the two parts of the statement that relates two units.

E QUIVALENCE S TATEMENT Equivalence Statement: equivalent measures from the English and Metric Systems. Example: 2.54 cm = 1 inch

E XAMPLE : C HOOSING C ONVERSION F ACTORS 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.

A NSWER : C HOOSING C ONVERSION F ACTORS 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.

Q UIZ T IME ! A) Is the following conversion to scientific notation correct? If not correct the scientific notation > 21.7 x 10 4 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? cm x 2.54cm/1inch or 1in/2.54 = ? Inches.

A NSWERS TO Q UIZ ! A) > 2.17 x 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) 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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