1. Rename one-eighth as a percent. (1 point) 1.25% 12.5% 125% 1250% 2. Rename .709 as a percent. (1 point) 709% 70.9% 79% 7.09% 3. What percent is equivalent to two-thirds?

Answers:
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1)   [B]:  "12.5%" .
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2)  [B]:  "70.9%" .
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3)  "66[tex] \frac{2}{3} [/tex]%" ;  or, "66.6666... % " ;  or, round to:  "66.667 %" ;
                     or; round to:  "66.67%" .
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Explanation:
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1)  "Rename one-eight as a percent". 
  
→  [tex] \frac{1}{8}[/tex] = 1 ÷ 8 = 0.125 ;

→ [tex] \frac{x}{100}[/tex] = 0.125 ;  
        
       →  x = 0.125 * 100 = {move the decimal point in the number, "0.125"; two spaces forward, since we are MULTIPLYING, by "100" (which has 2 zeros); 
       →  x = 12 * 100 = 12.5 .

So:  → [tex] \frac{12.5}{100}[/tex] = 12.5 % ;  since "12.5 % = 12.5/100 "
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Other method:
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     → [tex] \frac{x}{100}[/tex] = [tex] \frac{1}{8}[/tex] ; 

               →  x = 100 * [tex] \frac{1}{8}[/tex] ;

               →  x  = [tex] \frac{100}{1}[/tex] * [tex] \frac{1}{8}[/tex] ;

                         =   [tex] \frac{100*1}{1*8} [/tex] ;

                         =   [tex] \frac{100}{8} [/tex] ;

               →   x  =  12.5 ;

               →   [tex] \frac{x}{100} [/tex] = [tex] \frac{12.5}{100} [/tex] = 12.5% ;

                      → 12.5 % =  [tex] \frac{12.5}{100} [/tex] ; 
                                      =  ?

→ {Take the "12.5" & move the decimal backward TWO (2) places, since we              are "dividing" by "100" (which has 2 "zeros") ;
 
                                     = 0.125 = [tex] \frac{125}{100}[/tex] = [tex] \frac{1}{8} [/tex].
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2)  "Rename "0.709" as a percent."

===>  [tex] \frac{x}{100} [/tex] = 0.709 ;  

    → x = 0.709 * 100 = ? ;

Note:  Take the "0.709" ; & move the decimal place "2 (TWO)" spaces forward, since are MULTIPLYING by "100" (which has 2 zeros); to get:
    → x = 70.9 ;

    → x = 0.709 * 100 = 70.9  ;

→ [tex] \frac{x}{100} [/tex] =  [tex] \frac{70.9}{100} [/tex] = 70.9% ;
                                            → which is:  Answer choice:  [B] .

    →  70.9% = [tex] \frac{70.9}{100} [/tex] = ?  ; 

     {take the "70.9" ; and move the decimal point backwards TWO (2) decimal places; since we are DIVIDING by "100" (which has "2 (two) zeros") ;

    →  70.9% = [tex] \frac{70.9}{100} [/tex] = 0.709 .
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3)  What percent is equivalent to two-thirds? 
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    →  [tex] \frac{x}{100} [/tex] = [tex] \frac{2}{3} [/tex] ; 

x = [tex] \frac{2}{3} [/tex]*100 ;

    = [tex] \frac{2}{3} [/tex]*[tex] \frac{100}{1} [/tex] ;

    = [tex] \frac{2*100}{3*1} [/tex] ;

    = [tex] \frac{200}{3} [/tex] ;

    = 66[tex] \frac{2}{3} [/tex] ;

→  { 66[tex] \frac{2}{3} [/tex] } / 100 = 66 [tex] \frac{2}{3} [/tex] % ;  
                                                 or, write as:  66.666666....% ; or, round to:
                                                                      66.67% 
                               {since: " [tex] \frac{2}{3} [/tex] " = 2 ÷ 3 = 0.66666..." .
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