Comparing and Ordering Numbers

Pd. Comparing & Ordering Al\va con ert nwnb rs to а compar pln с nluc from U uall round to the neare t То change а percent to а decima\, mo е the decimal 1- plu с to thc CALCULATOR КЕУS NEGATIVE NUМВERS ➔ ALWAYS USE ТНЕ (-) ВUТТО ...NOT ТНЕ UBTRACTION SIG !!!! Fraction to Decima\: : ➔ S+-+D Exponents: -1 12 1 3 3- ➔ Absolute Va\ue 1 1: Abs 1-101➔ Repeating Bar - : АLРНА➔ Г 3.12 ➔ _в_ ,о Мixed numbers Percent % symbol: SНIFT ➔ ( 5% 3rr Pi 1t symbol: SНIFТ ➔ xlox Cube root V- symbol: SНIFТ ➔ Г Ех. 1) 1n each circle, place the correct symbol ( <, >, =). А) �G) 1. qч В _ ) 1� � 3 (J) _ -Ч.33 1. i'\ 1 rr 5 -ч.чо i }.%S -µ -ч. 5 Srr 4 .L, -2 (J) i.�3 9 0% о. q () ' -2 ' 3� } 1-� Vt3 it' ' 2s 3 � ➔ ➔ о.о� ч. Wз ➔ 3 (р D) 3.14 3, IЧ 0 1t .3. IЧ Ех. 3) List tbe numbers from greatest to least. Ех. 2) List the numbers from least to greatest. 14 { 3.85 , -4.5 , -3 С) 2 2 Ч/ -, ➔ -- 61%} v �' \,, 3,)r?> J3 1.5Ч PRACTICE: Comparing and Ordering Real Numbers 1.) List the numbers from least to greatest. { -6 , -21t , m , 45%, - 13 } "' � i - t,� -;, �� 2.) List the numbers from greatest to leas,t { -4 , 7%, 4.12 , - v19, -ЗVZ , } \, 1 o,;tt> -� t t, J, -;r -i, -tµ'(, � 0,,%1 � :)ИЧ - -t3 1. 3.) List the numbers from greatest to � 6.8 2rr v � lJЗ 5. ) 1Т 1- lc .i № "' 460% .1, J., � .!} 1f {5 5 Ч)I{> 1у3'и м Ч�О"/о t, 0.15 6.) \-О .Ч 1 Ъ S·IC) 0.15 Ф' oJМ'S � 5 List the numbers from least to greatest. 13 п 30 13 т 2 J, '1, � Jt 0)-4- о� OAS Z1Г 1-0.41 35% J,, � List the numbers from least to greatest. 4- 4.) List the numbers from least to greatest. iчi·lo \3 J, 1.)f-2. � � 2.7 .J,, 4, J.)½5 Ч Z-/з 242% - (24 '1.- µ?J 7,.1 Directions: Write each number as а decimal and then fill each circle in ,vith the coгrect symbol: <, >, or =. 7.) 5 11 @5 9 2 5.50 10.) 1t l..._ � j,\'\ � 5.5t, 3.14 8.) - ',' -З.111 f)\ - 3.72 \!_) -з.�1. 9.) ': � -3.5 Z.(,� \.._!_)-3.S uestions: Com & Orderin Real Numbers 1.) Two expressions аге shown belo\v . ../i .. J( For w hich value of х is the value of !4 greater than the value of ./х? Circle the correct answe r. Г�о� ч.ц1 2.) Four exp ressions are shown Ьelow. ..fi х 2х Which inequality oomparing two of the expressions is true when 0.3 < х < 0.5? Cirde the correct answer. 2(0.ч)�о.� (о.ч) \У о.ч 1. .,. O,lu С) 2х < ../х А)х2 > ..fx З.) Place the following expressio ns in огdег from least to greate st when О х .. .J;""t,�) ,. �', 1 / :, 5-х 5 -s о.\ - � < х < 0.2. О. 1 Sx 5-а., S (0.1) �� ::� � )( s sx Гsх 5-Х. PRACTICE: КEYSTONE PROBLEMS 1.) Two expressions аге shown below. Л.\ " / !! _ Fог which value of. is the value of тrх greater than the value of !!.7 Circle the correct answer. х }1 А) 0.3 - -= 10.ч1 о.� 2.) . Four expressions аге shown below. s) 3 1.. �\., Зх 3(0.S) �\,? � �� 0.\1 \Гзх (J(. о!:. 3 3 .. \.1,1.. х О. Which inequality comparing two of the expressions is true when 0.4 < х < 0.9? Circle the ,J, correct answer. о. 5" А) 3.) ..fзх > �з В) fu > Зх List the numbers from least to greatest. S1r 1-14.81 4 155 х С) Зх <­ з 4.) з D)х < Зх List the numbers from greatest to least. 27r � fi Simplifying Square Roots • When simplifying square roots, we want to divide any under the Г sign. ех.) Simplify per f-tc,,t S%\Л..A,V-t, factors out ofthe number ffl 1.) Make а list of perfect squares at the top of your paper: _\_, �. _j_, � � �, ч li , r� t v ч , 1!__, _!00_, ш , 1 ч ч I u9 perfect square that divides into the number under the V {S 2.) Find the \ С\ and factor it using that perfect square number and its other factor. Ве sure to put the perfect square factor 3.) Simplify the wARNING: t\ (Sf ре [fe(A square root but leave the second one the I If you do not use the а r�.es+ г perfect square factor, you will have to simplify it jчГ2J ех.) Ш i\ Гч�,, '1Ч [2. ·ш Directions: SimpШy each square root. 1) v44 /\ Гч [\", �[2�] 2) l\@/LIо . Dffi NOT USE LARGEST PERFECT SOUARE USED LARGEST PERFECT SOUARE ех. l\ ✓зоо I lio\) :: [о ' J3 fi) 3) -198 ,, r:: Jчq \J 1.. ;Gп l PRACTICE: SIМPLIFYING SOUARE ROOTS Directions: Fully simplify еасЬ square root. Sho,v all of your ,vork. Ве sure to first make а list of perte· ct squares to help you out! 1.) ../8 ,, �Ji =)1Ji 1 5.) ш -./и 1, �r Jq� fi I' .Гц ../99 /\ ../2б /' �Гs �J\i m 1, 7.) Js m 8.) 1, ✓1ов ,, 12.) Jq Гii �Е§ "3[ii f ' J1i -./1б � ��r� 11.) v4fJ /' Гч Г.о =12-!То ] .fq� JТlP[-Z. �J / �@) ��Js 1 10.) ' 4.) {8б {li; 2Г3 \ {�п\ 9.) 3.) Гч fi 6.) /"\ -:: 3[9: 2.) ' ✓200 / /\оо Ji � \10Jil z. [i 13.) ../2б 1, sчrs �[т 14.) .../98 1, № [1.. ?@] :;[L.�] 15.) ..д5 ,, fet Гs �� 16.) ../% 1, JТuГи �8Гu 1 �@ll\JJfшr��@X@� r�@��,W Directions: Estimate each square root to the nearest whole number. NO CALCULATOR!!!! ч -l. ...fif. @J q lli_ Чсt L,Ч Jj_ Зu -- 2.-../43 @] з. ..f59 @] 8"\ I_QQ_ � 1 ЧЧ \ t,q ..fso 4. ,, 5 . ...ffo / [Е1 {-i) [i � 6.'1зз @ 11. -../18 dt 7.ffi QE] 12. {6 �] 21. ✓з2 JI"� �@] 26. ✓500 I' [Гuь(s @ ../48 ,, flwз �@ 13. ../89 � �[ilil 16. v'123 8. 17. ../95 @ 22. ✓24 /' JЧ [v �[@ 21. ✓50 / \ _ri's (t 1[ш 18. ✓102 � 23. ✓44 / ' Jч� @ 28. ✓18 '\ Г\[t [@ 9 . .д;5 / ' 10. [@ 14. ../52 ;, 15.v'104 '" (ч fiu ��siv] [{lчi] 24. ✓12 I' {q [i :;�,, j.4Ji, 29.::;�'Z, 150 J\ Л?fi @] -Jы � Jч t°v 19. v'142 ' �[Zill 20. ../3 rnJ 25. ✓75 �w /' [isЛ 30. ✓125 I' (i"s Гs @J Simplifying More Complex Square Roots ч -3_ 1!L 12_ ov � !ri Ю_ LQQ._ 11:L � lutt Directions: Simplify each of the following square roots. - ,, Ех 1) 5../бз ЕхЗ) 0,..fio /\ Ех 2) 2'/2500 - ,, Jf5Jioo fffi [чfs --5 • -1 о =@о] ::Qsfi) 3J-i 2Js ��1Гs] ' Ех 5) 5_✓ 700 - ,, [fsS3 Ex4)-2...fis '\ [Гоо(l [qfs �.оп S-!3 ::\-10Г3 Ех б) -з-Дs /' \ зГs ��ofij =t9 1 ' Гs( , m. Which expression represents the -exact length of qi М Ех 10) А square has а side length of the square? Circle the correct answer • / ' F�Ji �1п А) 9.9 В) 2V7 D) 7../5 \с) 7'121 Ех 11) The length of а diagonal of а rectangle is svГz. Which number is equal to the length of the diagonal? Circle the correct answer. J s�:zб Гzs· Ji = Jso А) С)./zб Jo)../sol В)../29 М Ех 12) Which expression сап Ье simplified to 2 ✓п + 4 whe�e п is а positive integer? Circle the correct answer. zJi 250 .доl Гд) Ех 13) When х 3.[z6 3(1j) :-\5" A)Зfu = PJr✓8 3Ji 3,Гs ..вrт Дv18 S, which expression can Ье simplified to 15'12? Circle the correct answer. 3,fГots) ;№ sEГs) sJ\5 1. [t1" ,5fz. \в) з ✓1ох } - sji;Гs) S№ (t; (1. 2sJ1. С) Sffx D) 5✓10х PRACТICE: Simplifying More Complex Square Roots Directions: Simplify each of the following square roots. I ' Jц r,_ �}irc:) 4) ✓ 2so /" J[s[Гo = ,, 2) ✓-18 1) v'8 \sJlo] 7) 5 ✓ 144 {1-z,) 5. 1'2. � §] ,, [Ч /1\ i.fi". - 10) �-v'44 \1ori1l з)Ш '" /с1 [3 (ei fz. =[ill] �� б) ✓400 ,, Гч ,, fЧ (v -;[lГз} [iou S)ill Н)•2. = - ,, 8)-2-ИО 9) �[-l,�1 1 11)-f-v'З00 .fwu зvso /\ jf 1"Гt> 3Г�о ' [0 п \ 10Гз � �-l,o Гз } ill .[i 5'11. - :J1sГz/ ,,, [,о 1 12) 2-v'160 fii чfо ::\� № 1 13) The decimal approximation of ..ffo is а value between what two integers? Circle the correct answer. ,Ь � \fuЧ 51 t 4 � А) 6 and 7 В)7 and 8 /с) 8 and g J 14) Which expression is equivalent to 2..,fi? Circle the correct answer. D) 9 and 10 D)VЗZ с)ж lв)../28 l д}../98 15} А rectangle has а diagonal length of '145. Which expression represents the exact length of the diagonal? Circle the correct answer. jч5 ,, �Js ЗГs D) 6.71 C)2..,fi А) 5--./3 r В) З\l's / 16) Which expression сап Ье simplified to 5-Jr + 4 where r is а negative integer? Circle the correct answer. /чо '' Jчf\O 7,JIO A)ffo Jsч,, � fis f, fЧ� .� f[!./� � [j B)v54 С) -J125 /o) m r 3{<; ?{s G� ' ' : Simplifying Square Roots 1 •{;i Working Backwards �f ·· ·· -· -·· ·�· -·· - " " - " " - " " - " " - ." " - " ." .- • ·-·· Ве sure to SHO W ALL STEPS! Directions: Work backwards to f1nd the or1g1nal square root. -··-··-··-··-··-··-··-··-··-··-··-··-··-·, STEPS: . . . . . 1.) Write the WY\0\t number in square root form Ьу squarIng rt (mult1ply1ng ,t Ьу I }:f 2.) Multiply the numbers under the square гооt symbols together. ,eIf ). ...... 1.) What square root simplifies to: 2✓5 , i i Prove it z 1- -;; ч rч ·Гs � [J-Zё 1 '- 11 2.) What square root simplifies to: 3✓7 r РГОVе it 3'�q �·Гi�!Ju3J L.. 4.) What square root simplifies to: 2✓'13 5.) What square root simplifies to: б ✓З "11\ �� � 2 4✓ . "11\ � \.. 3.) What square root simplifies to: ......... r РГОVе it rРГОVе it 'L ч �1t.o (;2 = 3tJ J№.Ji ,[fiij =r f3u-J3 {П)i " 11 • . g square Roots Review si.rnplify each square root. ✓75,, {fs 41 2) , 6 ), � I' J1u� 1n / ' J3fi] ,, 3� 7) I '- -п @] � [i. 13) {за ,./и '" Гч 10) 14) - 3� / � /чЕL �sJs ..... 11) 7� ,, 8) , 12) 4� ,, - 2� ( ...... %(Jf3 ?��Гз] 16) ]Ef, 5.[, �[_io н l §] .fi fi (.,,.✓3 �ЕКJ 15) Г�в ' ' [JJiJ z,Ji. sfi @т rf} [@ [Z5fi ([Sfs V64 4) � fffiJ @J 9) {¼ 3) GJ @Ж) 5) \h6 5� ,, sчп 1,,,11 � For #17-20, state what square root simplifies to given number for еасЬ proЫem. SHOW ALL WORК! 17) зГs 2- � ::" f1· Гs �IFsl 18) бл/z m·Jl t, i-:. 3LP � [Inl 19), 2 .Js 2,�-:.ц JZt.� �[§] 20) 5� s�;is Гz5-� [iТ6D]