Video: Ordering Rational Numbers

Which of the following choices shows the amounts in order from the least to greatest? [A] 1/2, 65% of 1, 0.329 [B] 2/5, 0.31, 49% of 1 [C] 45% of 1, 0.5, 2/3 [D] 80% of 1, 3/4, 0.492

04:19

Video Transcript

Which of the following choices shows the amounts in order from the least to greatest? Is it (A) one-half, 65 percent of one, and 0.329; (B) two-fifths, 0.31, 49 percent of one; (C) 45 percent of one, 0.5, two-thirds, (D) 80 percent of one, three-quarters, and 0.492?

To work out whether the choices are in order from least to greatest, we need to convert all the values to either fractions, decimals, or percentages. In this question, we will convert them to decimals. Let’s begin by considering how we convert the percentages to decimals. The word “percent” means out of 100 and the word “of” in mathematics means multiply. Therefore, 65 percent of one is the same as 65 over 100 multiplied by one. Any number multiplied by one remains the same. Therefore, this is equal to 65 over 100.

As the line in a fraction means divide, we need to divide 65 by 100. We move all our digits two places to the right, giving us a decimal value 0.65. 65 percent of one is equal to 0.65. We could repeat this with 49 percent of one such that this is equal to 0.49. 45 percent of one is equal to 0.45. 80 percent of one is equal to 0.8 or 0.80.

We also need to convert the four fractions to decimals. Most of these are common fractions that we should know the conversions of. One-half is equal to 0.5. We know that one-fifth is equivalent to two-tenths. Therefore, it is equal to 0.2. This means that two-fifths is equal to 0.4. One-third is equal to 0.3 recurring. This can be denoted with a dot or bar above the three. Two-thirds is, therefore, equal to 0.6 recurring. Finally, we know that one-quarter is equal to 0.25 as this is a half of a half. Three-quarters is, therefore, three times this and it’s equal to 0.75.

We have now converted all of our values to decimals. We need to find the list that is in order from least to greatest. Option (A) is incorrect as 0.329 is less than 0.65 and 0.5. The same is true for option (B) as 0.31 is less than 0.4. In option (D), the numbers are in descending order. They’re going from greatest to least. 0.8 is greater than 0.75, which is also greater than 0.492.

The correct answer is, therefore, option (C). 0.45 is less than 0.5, which is less than 0.6 recurring. Option (C) shows the amounts in order from least to greatest, 45 percent of one, 0.5, and then two-thirds.

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