ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Converting Rational Number Forms
20 questions · exam conditions
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Converting Rational Number FormsQuestion 1 of 20

A value is increased by 150%. This is equivalent to multiplying the original value by what number, expressed as a fraction?

32\frac{3}{2}
52\frac{5}{2}
320\frac{3}{20}
2320\frac{23}{20}
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ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Converting Rational Number Forms

Practice Converting Rational Number Forms in ACCUPLACER Quantitative Reasoning, Algebra & Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Converting Rational Number Forms, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Quantitative Reasoning, Algebra & Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A value is increased by 150%. This is equivalent to multiplying the original value by what number, expressed as a fraction?

  1. 32\frac{3}{2}
  2. 52\frac{5}{2} (correct answer)
  3. 320\frac{3}{20}
  4. 2320\frac{23}{20}
Explanation: An increase of 150% means the new value is the original 100% plus the 150% increase, which totals 250% of the original value. To convert a percentage to a multiplier, convert it to a decimal: 250%=2.5250\% = 2.5. To express 2.5 as a fraction, write it as 2122\frac{1}{2}, which is equivalent to the improper fraction 52\frac{5}{2}.

Question 2

Which of the following lists numbers in order from least to greatest?

  1. 58,0.6,65%\frac{5}{8}, 0.6, 65\%
  2. 0.6,58,65%0.6, \frac{5}{8}, 65\% (correct answer)
  3. 58,65%,0.6\frac{5}{8}, 65\%, 0.6
  4. 0.6,65%,580.6, 65\%, \frac{5}{8}
Explanation: To compare the numbers, convert them all to the same format, such as decimals. 58=5÷8=0.625\frac{5}{8} = 5 \div 8 = 0.625. 65%=0.6565\% = 0.65. The number 0.6 is already a decimal. Now, order the decimals from least to greatest: 0.6, 0.625, 0.65. This corresponds to the original list: 0.6,58,65%0.6, \frac{5}{8}, 65\%.

Question 3

A baker uses 0.625 of a bag of flour for a recipe. What percentage of the flour is left in the bag?

  1. 12.5%
  2. 37.5% (correct answer)
  3. 62.5%
  4. 160%
Explanation: The entire bag of flour represents 100%, or 1. If 0.625 of the flour is used, the amount remaining is 1−0.625=0.3751 - 0.625 = 0.375. To express this decimal as a percentage, multiply by 100: 0.375×100%=37.5%0.375 \times 100\% = 37.5\%.

Question 4

A wire is 10.4 meters long. A piece measuring 3.9 meters is cut from it. What fraction of the original wire is left?

  1. 38\frac{3}{8}
  2. 58\frac{5}{8} (correct answer)
  3. 35\frac{3}{5}
  4. 23\frac{2}{3}
Explanation: First, calculate the length of the remaining wire: 10.4−3.9=6.510.4 - 3.9 = 6.5 meters. Next, express this remaining length as a fraction of the original length: 6.510.4\frac{6.5}{10.4}. To simplify this fraction, multiply the numerator and denominator by 10 to remove the decimals, resulting in 65104\frac{65}{104}. The greatest common divisor of 65 and 104 is 13. Simplifying the fraction gives 65÷13104÷13=58\frac{65 \div 13}{104 \div 13} = \frac{5}{8}.

Question 5

In a survey, 6.25% of respondents chose "other." What fraction of respondents chose "other"?

  1. 18\frac{1}{8}
  2. 116\frac{1}{16} (correct answer)
  3. 58\frac{5}{8}
  4. 254\frac{25}{4}
Explanation: To convert a percentage to a fraction, first write it as a decimal: 6.25%=0.06256.25\% = 0.0625. Then, write the decimal as a fraction based on its place value: 0.0625=625100000.0625 = \frac{625}{10000}. To simplify, divide the numerator and denominator by their greatest common divisor. Both are divisible by 625. 625÷625=1625 \div 625 = 1 and 10000÷625=1610000 \div 625 = 16. So, the simplified fraction is 116\frac{1}{16}.

Question 6

A stock valued at $48 per share loses 316\frac{3}{16} of its value in one day. What is the new value of the stock, expressed as a decimal?

  1. $9.00
  2. $39.00 (correct answer)
  3. $47.81
  4. $57.00
Explanation: First, calculate the amount of the loss: 316×48=14416=9\frac{3}{16} \times 48 = \frac{144}{16} = 9. The stock lost $9 in value. To find the new value, subtract the loss from the original value: 48−9=3948 - 9 = 39. Expressed as a decimal, the new value is $39.00.

Question 7

A chemical solution is 0.1375 acid by volume. What fraction of the solution is acid?

  1. 1180\frac{11}{80} (correct answer)
  2. 118\frac{11}{8}
  3. 27200\frac{27}{200}
  4. 320\frac{3}{20}
Explanation: To convert the decimal 0.1375 to a fraction, write it over its place value: 137510000\frac{1375}{10000}. To simplify, find the greatest common divisor or simplify in steps. Dividing the numerator and denominator by 25 gives 55400\frac{55}{400}. Dividing again by 5 gives the simplest form, 1180\frac{11}{80}.

Question 8

The fraction 57\frac{5}{7} is approximately 0.714285. Which of the following is the value of 5700\frac{5}{700}?

  1. 71.4285
  2. 0.0714285
  3. 0.00714285 (correct answer)
  4. 0.000714285
Explanation: The expression 5700\frac{5}{700} can be rewritten as 57×1100\frac{5}{7} \times \frac{1}{100}. Since 57\frac{5}{7} is approximately 0.714285, the value of 5700\frac{5}{700} is approximately 0.714285×11000.714285 \times \frac{1}{100}. Multiplying by 1100\frac{1}{100} is the same as dividing by 100, which shifts the decimal point two places to the left. Therefore, 0.714285÷100=0.007142850.714285 \div 100 = 0.00714285.

Question 9

What is 80% of 516\frac{5}{16}?

  1. 14\frac{1}{4} (correct answer)
  2. 12\frac{1}{2}
  3. 25
  4. 50
Explanation: To find 80% of a number, you multiply the number by 0.80. It's often easier to work with fractions. Convert 80% to a fraction: 80%=80100=4580\% = \frac{80}{100} = \frac{4}{5}. Now, multiply this fraction by 516\frac{5}{16}: 45×516=4×55×16=2080\frac{4}{5} \times \frac{5}{16} = \frac{4 \times 5}{5 \times 16} = \frac{20}{80}. Simplifying this fraction gives 14\frac{1}{4}.

Question 10

If xx is a number such that x÷0.8=54x \div 0.8 = \frac{5}{4}, what is xx expressed as a percentage?

  1. 1%
  2. 64%
  3. 100% (correct answer)
  4. 125%
Explanation: First, solve for xx. The equation is x0.8=54\frac{x}{0.8} = \frac{5}{4}. It is helpful to convert both numbers to the same format. As decimals, 54=1.25\frac{5}{4} = 1.25. The equation becomes x0.8=1.25\frac{x}{0.8} = 1.25. Multiply both sides by 0.8 to isolate xx: x=1.25×0.8=1x = 1.25 \times 0.8 = 1. To express the number 1 as a percentage, multiply by 100: 1×100%=100%1 \times 100\% = 100\%.

Question 11

In a group of people, 38\frac{3}{8} are students. Of the remaining people, 40% are teachers. What decimal represents the fraction of the whole group that are teachers?

  1. 0.25 (correct answer)
  2. 0.40
  3. 0.60
  4. 0.625
Explanation: First, find the fraction of the group that are not students. If 38\frac{3}{8} are students, then 1−38=581 - \frac{3}{8} = \frac{5}{8} are remaining people. Next, find the fraction of the group that are teachers by taking 40% of the remaining people. Convert 40% to a fraction: 40%=40100=2540\% = \frac{40}{100} = \frac{2}{5}. Now, multiply this by the fraction of remaining people: 25×58=1040=14\frac{2}{5} \times \frac{5}{8} = \frac{10}{40} = \frac{1}{4}. Finally, convert the fraction 14\frac{1}{4} to a decimal, which is 0.25.

Question 12

A scientist measures a quantity as 87.5% of a standard unit. She needs to express this measurement as a fraction with a denominator that is a power of 2. Which fraction in lowest terms satisfies this requirement?

  1. 175200\frac{175}{200}
  2. 1416\frac{14}{16}
  3. 78\frac{7}{8} (correct answer)
  4. 3540\frac{35}{40}
Explanation: When you encounter percentage problems requiring specific fraction formats, start by converting the percentage to a fraction, then manipulate it to meet the given constraints. Converting 87.5% to a fraction: 87.5%=87.5100=875100087.5\% = \frac{87.5}{100} = \frac{875}{1000}. To eliminate the decimal, multiply both numerator and denominator by 10, giving us 8751000\frac{875}{1000}. Now reduce this fraction to lowest terms by finding the greatest common factor. Since 875=7×125875 = 7 \times 125 and 1000=8×1251000 = 8 \times 125, we get 8751000=78\frac{875}{1000} = \frac{7}{8}. Notice that 8 is 232^3, which is indeed a power of 2, and the fraction is in lowest terms since 7 and 8 share no common factors. Looking at the wrong answers: Choice A, 175200\frac{175}{200}, reduces to 78\frac{7}{8} but isn't in lowest terms as presented, and 200 isn't a power of 2. Choice B, 1416\frac{14}{16}, also reduces to 78\frac{7}{8} but isn't in lowest terms—you can divide both numerator and denominator by 2. Choice D, 3540\frac{35}{40}, reduces to 78\frac{7}{8} as well, but 40 isn't a power of 2, and it's not in lowest terms. The answer is C: 78\frac{7}{8}. Strategy tip: When working with percentages involving decimals like 87.5%, look for patterns—87.5% is exactly 78\frac{7}{8}, just as 12.5% is 18\frac{1}{8}, 25% is 14\frac{1}{4}, etc. Memorizing these common fraction-percentage equivalents saves time on standardized tests.

Question 13

A student incorrectly converts the fraction 712\frac{7}{12} to a percentage by first converting to the decimal 0.58, then multiplying by 100 to get 58%. What was the student's error, and what is the correct percentage?

  1. The student rounded too early; the correct answer is 58.33% (correct answer)
  2. The student used long division incorrectly; the correct answer is 58.67%
  3. The student confused the numerator and denominator; the correct answer is 58.17%
  4. The student calculated correctly; 58% is the right answer
Explanation: 712=7÷12=0.58333...\frac{7}{12} = 7 \div 12 = 0.58333... The student rounded 0.58333... to 0.58 too early in the process. The correct percentage is 0.58333...×100%=58.33%0.58333... \times 100\% = 58.33\% (or 5813%58\frac{1}{3}\%). Choice B gives an incorrect decimal conversion. Choice C would result from calculating 127\frac{12}{7} instead, but that doesn't give 58.17%. Choice D is incorrect since the student did make an error.

Question 14

A calculator displays the result 0.1428571429 when computing 17\frac{1}{7}. If this decimal pattern continues indefinitely, what is 37\frac{3}{7} as a percentage, rounded to the nearest tenth of a percent?

  1. 42.7%
  2. 43.0%
  3. 42.8%
  4. 42.9% (correct answer)
Explanation: When you encounter repeating decimals, you're working with fractions that don't convert to terminating decimals. The key insight here is recognizing the repeating pattern and using it to find related fractions. The calculator shows 17=0.1428571429...\frac{1}{7} = 0.1428571429... where the digits 142857 repeat infinitely. This is written as 0.142857‾0.\overline{142857}. To find 37\frac{3}{7}, you can multiply this repeating decimal by 3: 37=3×17=3×0.142857‾\frac{3}{7} = 3 \times \frac{1}{7} = 3 \times 0.\overline{142857}. Multiplying each digit in the repeating block by 3 gives us 3×142857 = 428571. However, we need to handle the carrying properly. Working through the multiplication: 3×0.142857‾=0.428571‾3 \times 0.\overline{142857} = 0.\overline{428571}, which equals approximately 0.4285714286. Converting to a percentage: 0.4285714286 × 100% = 42.85714286%. Rounded to the nearest tenth of a percent, this gives us 42.9%. Looking at the wrong answers: Choice A (42.7%) rounds too far down, missing the precision needed. Choice B (43.0%) rounds up too aggressively, likely from imprecise decimal work. Choice C (42.8%) stops at the hundredths place before applying the rounding rule correctly to the tenths place. For repeating decimal problems, remember that you can often work with the pattern arithmetically rather than converting to exact fractions. Also, pay careful attention to rounding instructions—"nearest tenth of a percent" means one decimal place in your final percentage.

Question 15

Express 0.234‾0.\overline{234} as a fraction, then determine which of the following fractions is equivalent to half of that result.

  1. 117999\frac{117}{999}
  2. 39333\frac{39}{333}
  3. 78666\frac{78}{666}
  4. 2341998\frac{234}{1998} (correct answer)
Explanation: Let x=0.234‾x = 0.\overline{234}. Then 1000x=234.234‾1000x = 234.\overline{234}. Subtracting: 1000x−x=2341000x - x = 234, so 999x=234999x = 234 and x=234999x = \frac{234}{999}. Half of this is 12×234999=2341998\frac{1}{2} \times \frac{234}{999} = \frac{234}{1998}. Choice A is the original fraction, not half. Choice B simplifies incorrectly. Choice C doubles the denominator but keeps the same numerator, which would give one-half, but uses wrong values.

Question 16

A recipe calls for 38\frac{3}{8} cup of flour, but Maria's measuring cup only shows decimal markings. She needs to convert this fraction to a decimal and then determine what percentage of a full cup this represents. What is the percentage?

  1. 37.5% (correct answer)
  2. 38.3%
  3. 35.8%
  4. 40.0%
Explanation: First convert 38\frac{3}{8} to decimal: 3÷8=0.3753 \div 8 = 0.375. Then convert to percentage: 0.375×100%=37.5%0.375 \times 100\% = 37.5\%. Choice B results from rounding 38\frac{3}{8} incorrectly to 0.383. Choice C comes from miscalculating 3÷83 \div 8 as 0.358. Choice D results from confusing 38\frac{3}{8} with 25\frac{2}{5}.

Question 17

When 116\frac{11}{6} is written in decimal form and rounded to three decimal places, the result is 1.833. If this rounded decimal is then converted back to a fraction in lowest terms, what fraction is obtained?

  1. 116\frac{11}{6}
  2. 611333\frac{611}{333}
  3. 18331000\frac{1833}{1000} (correct answer)
  4. 1833999\frac{1833}{999}
Explanation: This question tests your understanding of decimal-to-fraction conversion and the distinction between exact values and rounded approximations. When you convert the rounded decimal 1.833 back to a fraction, you need to work with what you actually have: the three-decimal-place number 1.833, not the original fraction 116\frac{11}{6}. To convert 1.833 to a fraction, recognize that this decimal has three places after the decimal point, so it equals 18331000\frac{1833}{1000}. You can verify this isn't in lowest terms by checking if 1833 and 1000 share common factors. Since 1833 = 3 × 611 and 1000 = 8 × 125, they share no common factors, so 18331000\frac{1833}{1000} is already in lowest terms. Looking at the wrong answers: Choice A (116\frac{11}{6}) represents the original fraction before rounding, but the question asks what you get when converting the rounded decimal back. Choice B (611333\frac{611}{333}) appears to come from incorrectly factoring or manipulating the numbers. Choice D (1833999\frac{1833}{999}) uses the wrong denominator—999 would be used if you were dealing with a repeating decimal, but 1.833 is a terminating decimal. The key strategy here is to read carefully: you're not finding an equivalent to the original fraction, but rather converting a specific rounded decimal. When converting terminating decimals to fractions, the denominator is always a power of 10 based on the number of decimal places.

Question 18

A team wins 6 of its 11 games. What decimal represents the fraction of games the team won?

  1. 0.54
  2. 0.54‾\overline{4}
  3. 0.54‾\overline{54} (correct answer)
  4. 0.55
Explanation: To convert the fraction 611\frac{6}{11} to a decimal, divide the numerator by the denominator: 6÷116 \div 11. The result of the division is 0.545454...0.545454.... In this decimal, the block of digits '54' repeats indefinitely. The correct notation for this repeating decimal is 0.54‾0.\overline{54}.

Question 19

A number yy is equal to 0.23‾0.2\overline{3}. What is yy expressed as a fraction?

  1. 23100\frac{23}{100}
  2. 2399\frac{23}{99}
  3. 730\frac{7}{30} (correct answer)
  4. 14\frac{1}{4}
Explanation: To convert the repeating decimal 0.23‾0.2\overline{3} to a fraction, set y=0.2333...y = 0.2333.... Multiply by 10 to isolate the repeating part: 10y=2.333...10y = 2.333.... Multiply by 100 to shift the decimal again: 100y=23.333...100y = 23.333.... Subtract the first equation from the second: 100y−10y=23.333...−2.333...100y - 10y = 23.333... - 2.333..., which simplifies to 90y=2190y = 21. Solve for yy: y=2190y = \frac{21}{90}. Simplify the fraction by dividing the numerator and denominator by 3: y=730y = \frac{7}{30}.

Question 20

If a=0.75a = 0.75, b=15b = \frac{1}{5}, and c=150%c = 150\%, what is the value of a−bca - bc?

  1. −2120-\frac{21}{20}
  2. 920\frac{9}{20} (correct answer)
  3. 35\frac{3}{5}
  4. 12\frac{1}{2}
Explanation: First, convert all values to a single format, like fractions. a=0.75=34a = 0.75 = \frac{3}{4}. b=15b = \frac{1}{5}. c=150%=1.5=32c = 150\% = 1.5 = \frac{3}{2}. Now substitute these into the expression: a−bc=34−(15×32)a - bc = \frac{3}{4} - \left(\frac{1}{5} \times \frac{3}{2}\right). Following the order of operations, perform the multiplication first: 15×32=310\frac{1}{5} \times \frac{3}{2} = \frac{3}{10}. Now perform the subtraction: 34−310\frac{3}{4} - \frac{3}{10}. Find a common denominator, which is 20: 1520−620=920\frac{15}{20} - \frac{6}{20} = \frac{9}{20}.