1. Which of the following best represents the speed of a banana slug?
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1 Scientific Notation 1. Which of the following best represents the speed of a banana slug? A kilometers per second B meters per second C meters per second D kilometers per second 2. The equatorial radius of Mars is 3,394 km. Which of the following would be a reasonable estimate for the equatorial radius of Mars? A km B km C km D km 3. The display on a calculator screen is shown below EE9 What number does the calculator display represent? A. 3,375,080,000 B C. 337,508,000,000,000 D Visible blue light has a wavelength of about centimeters. What is this measurement written in scientific notation? A centimeters B centimeters C centimeters D centimeters 5. The display on a calculator screen is shown below.
2 EE-6 What number does the calculator display represent? A B. 375,187.2 C D. 3,751, Which shows the expression below simplified? A B C D ( ) 8. The Earth is approximately km from Venus at its closest approach. The Earth is also about km from Proxima Centauri, a star. Which of the following is true? A. The distance from Earth to Proxima Centauri is approximately two trillion times the distance from Earth to Venus. B. The distance from Earth to Proxima Centauri is approximately two billion times the distance from Earth to Venus. C. The distance from Earth to Proxima Centauri is approximately two thousand times the distance from Earth to Venus. D. The distance from Earth to Proxima Centauri is approximately two million times the distance from Earth to Venus. 9. The length of an object is measured as 24.7 centimeters. What is this measurement in scientific notation? A centimeters B centimeters C centimeters
3 D. 2, centimeters 10. Which shows the expression below in simplified form? A B C D ( ) ( ) Answers 1. C 2. D 3. A 4. B 5. A 6. B 8. D 9. B 10. A Explanations 1. A banana slug moves very slowly, so its speed is best represented by a very small number. Therefore, meters per second best represents the speed of a banana slug. 2. First, round the radius of Mars to the thousands place. Then, write each option in standard notation. 3,394 km 3,000 km km = km km = km km = 3,000 km km = 30,000 km
4 Therefore, km is the best estimate for the equatorial radius of Mars. 3. The calculator display represents a number in scientific notation where 10 is raised to the power given after the EE symbol EE9 = Convert the number to standard notation by moving the decimal point 9 places to the right = 3,375,080,000 Therefore, the calculator display represents the number 3,375,080, A number is written in scientific notation when it is expressed in the form shown below, where a is greater than or equal to 1 and less than 10, and n is an integer. a 10 n To write as a number greater than or equal to 1 and less than 10, move the decimal point 5 places to the right, and then multiply by 10-5 to offset moving the decimal point centimeters = centimeters 5. The calculator display represents a number in scientific notation where 10 is raised to the power given after the EE symbol EE-6 = Convert the number to standard notation by moving the decimal point 6 places to the left = Therefore, the calculator display represents the number First, convert to scientific notation ( ) = ( ) + ( ) Next, convert ( ) so the exponent is the same as the exponent in the second number. Then, complete the addition. Finally, convert to scientific notation. ( ) + ( ) = ( ) + ( ) ( ) + ( ) =
5 = Convert all of the values in scientific notation to standard notation. To help visualize this, think of it in terms of meters instead of millimeters. Remember, 1 meter is equal to 1,000 millimeters. The only reasonable option is 5.6 meters per second, or slow.. The other options are too 8. Compare the distance from Earth to Proxima Centauri to the distance from Earth to Venus by dividing the distance to Proxima Centauri by the distance to Venus. Since is equal to 2,000,000, the distance from Earth to Proxima Centauri is approximately two million times the distance from Earth to Venus. 9. A number is written in scientific notation when it is expressed in the form shown below, where a is greater than or equal to 1 and less than 10, and n is an integer. a 10 n To write 24.7 centimeters as a number greater than or equal to 1 and less than 10, move the decimal point 1 place to the left, and then multiply by 10 1 to offset moving the decimal point centimeters = centimeters 10. First, group the numbers multiplied by powers of 10 together, and then group the powers of 10 together. ( ) ( ) = (6 4) ( ) Then, multiply the numbers in the first set of parentheses and add the exponents of 10. Finally, convert to scientific notation. (6 4) ( ) = (-2) =
6 = Therefore, the simplified expression is
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