Question

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?

Answer 1

Answers:
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1) [B]: "12.5%" .
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2) [B]: "70.9%" .
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3) "66
`(2)/(3)`%" ; or, "66.6666... % " ; or, round to: "66.667 %" ;
or; round to: "66.67%" .
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Step-by-step explanation:
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1) "Rename one-eight as a percent".

→
`(1)/(8)` = 1 ÷ 8 = 0.125 ;

→
`(x)/(100)` = 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: →
`(12.5)/(100)` = 12.5 % ; since "12.5 % = 12.5/100 "
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Other method:
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→
`(x)/(100)` =
`(1)/(8)` ;

→ x = 100 *
`(1)/(8)` ;

→ x =
`(100)/(1)` *
`(1)/(8)` ;

=
`(100*1)/(1*8)` ;

=
`(100)/(8)` ;

→ x = 12.5 ;

→
`(x)/(100)` =
`(12.5)/(100)` = 12.5% ;

→ 12.5 % =
`(12.5)/(100)` ;
= ?

→ {Take the "12.5" & move the decimal backward TWO (2) places, since we are "dividing" by "100" (which has 2 "zeros") ;

= 0.125 =
`(125)/(100)` =
`(1)/(8)`.
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2) "Rename "0.709" as a percent."

===>
`(x)/(100)` = 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 ;

→
`(x)/(100)` =
`(70.9)/(100)` = 70.9% ;
→ which is: Answer choice: [B] .

→ 70.9% =
`(70.9)/(100)` = ? ;

{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% =
`(70.9)/(100)` = 0.709 .
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3) What percent is equivalent to two-thirds?
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→
`(x)/(100)` =
`(2)/(3)` ;

x =
`(2)/(3)`*100 ;

=
`(2)/(3)`*
`(100)/(1)` ;

=
`(2*100)/(3*1)` ;

=
`(200)/(3)` ;

= 66
`(2)/(3)` ;

→ { 66
`(2)/(3)` } / 100 = 66
`(2)/(3)` % ;
or, write as: 66.666666....% ; or, round to:
66.67%
{since: "
`(2)/(3)` " = 2 ÷ 3 = 0.66666..." .
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