The answer is: [C]: -0.7, ⅕, 0.35, ⅔ . ________________________________________ Explanation: _________________________________________ <span> Note that in this correct Answer choice "C" given, we have the following arrangement of numbers: _____________________________________________________ </span>→ -0.7, ⅕, 0.35, ⅔ ; ______________________________________ We are asked to find the "Answer choice" (or, perhaps, "Answer choices?") given that show a set of numbers arranged in order from "least to greatest"; that is, starting with a value that is the smallest number in the arrangement, and sequentially progressing, in order from least to greatest, with the largest (greatest) number in the arrangement appearing as the last number in the arrangement. ______________________ Note the EACH of the 4 (four) answer choices given consists of an arrangement with ONLY one negative number, "- 0.7". Only TWO of the answer choices—Choices "B" and "C"—have an arrangement beginning with the number, "-0.7 "; So we can "rule out" the "Answer choices: [A] and [D]". ________________________ Let us examine: Answer choice: [B]: <span>-0.7, 0.35, ⅕, ⅔ ; </span>_________________________ Note: The fraction, "⅕" = "2/10"; or, write as: 0.2 . ________________________________________ The fraction, "⅔" = 0.6666667 (that is 0.6666... repeating; so we often see a "final decimal point" rounded to "7" at some point. ___________________________________________ Through experience, one will be able to automatically look at these 2 (two) fractions and immediately know their "decimal equivalents". ____________________________________________ Otherwise, one can determine the "decimal form" of these values on a calculator by division: _________________________ → ⅕ = 1/5 = 1 ÷ 5 = 0.2 _________________________ → ⅔ = 2/3 = 2 ÷ 3 = 0.6666666666666667 ___________________________________ For Answer choice: [B], we have: ______________________________ → -0.7, 0.35, ⅕, ⅔ ; _________________________ → So, we can "rewrite" the arrangement of "Answer choice [B]" as: ___________________________________________ → -0.7, 0.35, 0.2, 0.666666667 ; ________________________________ → And we can see that "Answer choice: [B]" is INCORRECT; because "0.2" (that is, "⅕"), is LESS THAN "0.35". So, "0.35" should not come BEFORE "⅕" in the arrangement that applies correctly to the problem. _______________________________________ Let us examine: Answer choice: [C]: -0.7, ⅕, 0.35, 0.666666667 . ____________________________________________ → Remember from our previous— and aforementioned—examination of "Answer Choice: [B]" ; that: ____________________________ → ⅕ = 0.2 ; and: → ⅔ = 0.666666667 _______________________ So, given: ____________ → Answer choice: [C]: -0.7, ⅕, 0.35, ⅔ ; ______________________ → We can "rewrite" this given "arrangement", substituting our known "decimal values for the fractions: ______________________________ → Answer choice: [C]: -0.7, 0.2, 0.35, 0.666666667 ; _________________________________________ → As mentioned above, this sequence starts with "-0.7", which is the ONLY negative number in the sequence; as such, the next positive number is correct. Nonetheless, "0.2" (or, "(⅕") is the next number in the sequence, and is greater than "-0.7". The next number is "0.35. "0.35" is greater than "⅕" (or, "0.2"). Then next number is "(⅔)" (or, "0.666666667"). "(⅔)"; (or, "0.666666667") is greater than 0.35. ____________________________ This set of numbers: "-0.7, ⅕, 0.35, ⅔" ; is arranged in order from least to greatest; which is "Answer choice: [C]: -0.7, ⅕, 0.35, ⅔" ; the correct answer. ________________________________________________________
