Victory for the ACT Student Text 15e

L ESSON 1 | N UMBER AND Q UANTITY • 211

SCIENTIFIC NOTATION

20. Which of the following is equivalent to ( ) 120 10 5

21. A sound wave travels at approximately 1,125 feet/second. If a person hears a sound 2 2 1 minutes after it happens, how far away, in feet, is the person from the source of the sound? A. .1 6875 10 1 #

? F. .1 2 10 7 # G. .1 2 10 6 # H. .1 2 10 6 # J. .1 2 10 7 # K. .1 2 10 8 # The Cambridge Edge Know how to use your calculator –‘ †‘ •…‹‡–‹ϐ‹… notation problems. Some calculators allow you to input the numbers in •…‹‡–‹ϐ‹…‘–ƒ–‹‘ and return the product in •…‹‡–‹ϐ‹…‘–ƒ–‹‘ ƒ• ™‡ŽŽǤ ˆ ›‘— †‘ǯ– have a calculator that takes •…‹‡–‹ϐ‹…‘–ƒ–‹‘ inputs, then use the calculator to multiply the …‘‡ˆϐ‹…‹‡–•Ǥ COMPLEX NUMBERS

B. .2 8125 10 3 # C. .2 8125 10 4 # D. .1 6875 10 5 # E. .1 6875 10 6 #

Throwback to Math Class

, multiply the tens together by ǡ —Ž–‹’Ž› –Š‡…‘‡ˆϐ‹…‹‡–• ƒ† ƒ†† –Š‡ ‡š’‘‡–•Ǥ , subtract the exponents. ǡ †‹˜‹†‡ –Š‡…‘‡ˆϐ‹…‹‡–• ƒ† •—„–”ƒ…– –Š‡ ‡š’‘‡–•Ǥ

‘ —Ž–‹’Ž› ƒ —„‡” ‹ •…‹‡–‹ϔ‹…‘–ƒ–‹‘ „› ͷͶ –‘ ƒ ’‘™‡” adding the exponents. ‘ —Ž–‹’Ž› –™‘ —„‡”• ‹ •…‹‡–‹ϔ‹…‘–ƒ–‹‘ ‘ †‹˜‹†‡ ƒ —„‡” ‹ •…‹‡–‹ϔ‹…‘–ƒ–‹‘ „› ͷͶ –‘ ƒ ’‘™‡”

‘ †‹˜‹†‡ –™‘ —„‡”• ‹ •…‹‡–‹ϔ‹…‘–ƒ–‹‘

Which of the following expressions is equivalent to ( ) ( ) i i 3 4 3 + − , where i 1 = − 2 ? F. i 12 3 2 G. i 12 3 2 H. i 9 5 2 J. i 9 5 K. i 15 5

Which of the following expressions is equivalent to i 2 1 , where i 1 = − ? A. –2 B. –1 C. i 5 D. i 5 2 E. i 3 2

22.

23.

Throwback to Math Class Memorize these imaginary number values: i = 1 − i 1 = − 2 i = − 1 3 − i 1 4