ACCUPLACER Arithmetic Quiz: Comparing Fractions Decimals And Percents
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Comparing Fractions Decimals And PercentsQuestion 1 of 20

In a class election, Candidate A received 35% of the votes, Candidate B received 25\frac{2}{5} of the votes, and Candidate C received the remaining votes. Which of the following statements is true?

Candidate A received more votes than Candidate B.
Candidate B and Candidate C received the same number of votes.
Candidate C received the fewest votes.
Candidate B received the fewest votes.
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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Comparing Fractions Decimals And Percents

Practice Comparing Fractions Decimals And Percents in ACCUPLACER Arithmetic 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 Comparing Fractions Decimals And Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Arithmetic.

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

In a class election, Candidate A received 35% of the votes, Candidate B received 25\frac{2}{5} of the votes, and Candidate C received the remaining votes. Which of the following statements is true?

  1. Candidate A received more votes than Candidate B.
  2. Candidate B and Candidate C received the same number of votes.
  3. Candidate C received the fewest votes. (correct answer)
  4. Candidate B received the fewest votes.
Explanation: First, convert all vote shares to percentages. Candidate A has 35%. Candidate B has 25=40100=40%\frac{2}{5} = \frac{40}{100} = 40\%. To find Candidate C's share, subtract the others from 100%: 100%35%40%=25%100\% - 35\% - 40\% = 25\%. So, A=35%, B=40%, C=25%. Comparing these, Candidate C's 25% is the smallest share. Therefore, Candidate C received the fewest votes.

Question 2

Which of the following numbers is greater than 13\frac{1}{3} and less than 40%?

  1. 0.3
  2. 38\frac{3}{8} (correct answer)
  3. 25\frac{2}{5}
  4. 41%
Explanation: First, convert the given boundaries to a common format, like decimals. 13\frac{1}{3} is approximately 0.333...0.333.... 40%40\% is 0.400.40. The question asks for a number between 0.333...0.333... and 0.400.40. Now, convert the answer choices: A is 0.30.3, B is 38=0.375\frac{3}{8} = 0.375, C is 25=0.40\frac{2}{5} = 0.40, and D is 41%=0.4141\% = 0.41. The only value that falls between 0.333...0.333... and 0.400.40 is 0.3750.375.

Question 3

Which of the following numbers is the smallest?

  1. 1320\frac{13}{20} (correct answer)
  2. 66%
  3. 23\frac{2}{3}
  4. 0.67
Explanation: To find the smallest number, convert all options to decimals. A: 1320=13÷20=0.65\frac{13}{20} = 13 \div 20 = 0.65. B: 66%=0.6666\% = 0.66. C: 23=2÷3=0.666...\frac{2}{3} = 2 \div 3 = 0.666.... D: 0.670.67. Comparing the decimals 0.650.65, 0.660.66, 0.666...0.666..., and 0.670.67, the smallest value is 0.650.65.

Question 4

Which list shows the numbers 710\frac{7}{10}, 0.72, and 68% in order from greatest to least?

  1. 68%, 710\frac{7}{10}, 0.72
  2. 710\frac{7}{10}, 0.72, 68%
  3. 0.72, 68%, 710\frac{7}{10}
  4. 0.72, 710\frac{7}{10}, 68% (correct answer)
Explanation: Convert all numbers to decimals to compare them. 710=0.7\frac{7}{10} = 0.7. 0.720.72 is already a decimal. 68%=0.6868\% = 0.68. The three numbers are 0.70.7, 0.720.72, and 0.680.68. Ordering them from greatest to least gives 0.720.72, 0.70.7, 0.680.68. This corresponds to the original list: 0.72, 710\frac{7}{10}, 68%.

Question 5

A carpenter has two drill bits. One is 38\frac{3}{8} inch in diameter, and the other is 0.35 inches in diameter. The carpenter needs to drill a hole that is larger than 0.36 inches. Which drill bit, if any, can be used?

  1. Only the 38\frac{3}{8} inch bit can be used. (correct answer)
  2. Only the 0.35 inch bit can be used.
  3. Both drill bits can be used.
  4. Neither drill bit can be used.
Explanation: The hole must be larger than 0.36 inches. We need to compare the diameters of the two drill bits to this requirement. The second bit is 0.35 inches. Since 0.35<0.360.35 < 0.36, it is too small. For the first bit, convert the fraction 38\frac{3}{8} to a decimal: 3÷8=0.3753 \div 8 = 0.375. Since 0.375>0.360.375 > 0.36, this drill bit is large enough. Therefore, only the 38\frac{3}{8} inch bit can be used.

Question 6

A store offers two discounts on an appliance. The first offer is 30% off the original price. The second offer is 14\frac{1}{4} off the original price. Which statement accurately compares the two offers?

  1. The 30% off offer is a better discount. (correct answer)
  2. The 14\frac{1}{4} off offer is a better discount.
  3. Both offers provide the same discount.
  4. The better offer cannot be determined without the price.
Explanation: To compare the discounts, convert them to the same format. The first discount is 30%. The second discount is 14\frac{1}{4}, which is equivalent to 25100\frac{25}{100} or 25%. Since 30% is a larger value than 25%, the 30% off offer is a better discount for the customer. The actual price of the appliance is not needed to compare the rates of discount.

Question 7

A recipe requires 34\frac{3}{4} cup of flour. A baker has a measuring cup that holds 0.8 cups of flour when full. If the baker fills this cup, how does the amount of flour compare to the recipe's requirement?

  1. The baker has less than the required amount.
  2. The baker has exactly the required amount.
  3. The baker has more than the required amount. (correct answer)
  4. It is impossible to compare the amounts.
Explanation: To compare the amounts, convert the fraction to a decimal. 34=3÷4=0.75\frac{3}{4} = 3 \div 4 = 0.75. The recipe requires 0.75 cups of flour. The baker has 0.8 cups of flour. Since 0.8>0.750.8 > 0.75, the baker has more than the required amount.

Question 8

A survey shows that 920\frac{9}{20} of students prefer online classes, 0.460.46 prefer hybrid classes, and 45%45\% prefer in-person classes. If a student claims that hybrid classes are the most preferred, is this claim correct?

  1. Yes, because 0.460.46 is larger than both 920\frac{9}{20} and 45%45\% (correct answer)
  2. No, because 920\frac{9}{20} represents the largest preference group
  3. No, because 45%45\% represents the largest preference group
  4. The claim cannot be determined without additional calculations
Explanation: Convert to decimals: 920=0.45\frac{9}{20} = 0.45, 0.46=0.460.46 = 0.46, 45%=0.4545\% = 0.45. Hybrid classes at 0.460.46 have the highest preference. The claim is correct. Choice B incorrectly identifies online as largest. Choice C incorrectly identifies in-person as largest. Choice D suggests the comparison cannot be made, which is false.

Question 9

A basketball player's statistics show field goal percentages of 512\frac{5}{12} in the first quarter, 0.420.42 in the second quarter, and 41.5%41.5\% in the third quarter. In which quarter was the shooting percentage closest to 42%42\%?

  1. First quarter, because 512\frac{5}{12} is approximately 42%42\%
  2. Third quarter, because 41.5%41.5\% is closest to 42%42\%
  3. Second quarter, because 0.420.42 equals exactly 42%42\% (correct answer)
  4. All quarters are equally close to 42%42\%
Explanation: When comparing percentages given in different formats, you need to convert everything to the same format before determining which is closest to your target value. Let's convert all three shooting percentages to the same format as our target of 42%42\%. For the first quarter: 512=5÷12=0.4167...\frac{5}{12} = 5 ÷ 12 = 0.4167... which equals approximately 41.67%41.67\% For the second quarter: 0.420.42 as a decimal equals 42%42\% (since 0.42=42100=42%0.42 = \frac{42}{100} = 42\%) For the third quarter: 41.5%41.5\% is already in percentage form Now compare each to 42%42\%:
  • First quarter: 41.67%41.67\% differs by about 0.33%0.33\%
  • Second quarter: 42%42\% differs by exactly 0%0\%
  • Third quarter: 41.5%41.5\% differs by 0.5%0.5\%
Choice C is correct because 0.420.42 converts to exactly 42%42\%, making the difference zero. Choice A is wrong because 51241.67%\frac{5}{12} ≈ 41.67\%, not 42%42\%. Choice B is incorrect because while 41.5%41.5\% is close to 42%42\%, it's not the closest—it differs by 0.5%0.5\%. Choice D is wrong because the quarters clearly have different distances from 42%42\%. Study tip: When comparing values in different formats (fractions, decimals, percentages), always convert to a common format first. Remember that moving between decimals and percentages involves multiplying or dividing by 100: 0.42=42%0.42 = 42\%.

Question 10

An investor compares three mutual funds with annual returns of 325\frac{3}{25}, 12.5%12.5\%, and 0.1210.121. To maximize returns, which fund should be chosen, and what is the difference between the highest and lowest returns?

  1. Choose the fund with 12.5%12.5\% return; difference is 0.0050.005 (correct answer)
  2. Choose the fund with 0.1210.121 return; difference is 0.0050.005
  3. Choose the fund with 12.5%12.5\% return; difference is 0.0040.004
  4. Choose the fund with 325\frac{3}{25} return; difference is 0.0050.005
Explanation: Convert to decimals: 325=0.12\frac{3}{25} = 0.12, 12.5%=0.12512.5\% = 0.125, 0.121=0.1210.121 = 0.121. Highest return is 0.1250.125 (12.5%). Lowest is 0.120.12. Difference: 0.1250.12=0.0050.125 - 0.12 = 0.005. Choose 12.5% fund. Choice B incorrectly identifies 0.121 as highest. Choice C has wrong difference calculation. Choice D incorrectly identifies the fraction as highest return.

Question 11

A quality control inspector found that 1125\frac{11}{25} of widgets from Machine A, 0.4450.445 of widgets from Machine B, and 44%44\% of widgets from Machine C met specifications. Which machine produced the highest proportion of acceptable widgets?

  1. Machine A, because 1125=0.44\frac{11}{25} = 0.44 is the highest rate
  2. Machine B, because 0.4450.445 is the highest rate (correct answer)
  3. Machine C, because 44%=0.4444\% = 0.44 is the highest rate
  4. Machines A and C tie for highest, both at 0.440.44
Explanation: Convert to decimals: Machine A: 1125=0.44\frac{11}{25} = 0.44, Machine B: 0.4450.445, Machine C: 44%=0.4444\% = 0.44. Machine B has the highest rate at 0.4450.445. Choice A incorrectly identifies Machine A as highest. Choice C incorrectly identifies Machine C as highest. Choice D incorrectly claims A and C tie, ignoring that B is higher.

Question 12

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

  1. 0.3,25,35%0.3, \frac{2}{5}, 35\%
  2. 0.3,35%,250.3, 35\%, \frac{2}{5} (correct answer)
  3. 25,35%,0.3\frac{2}{5}, 35\%, 0.3
  4. 35%,0.3,2535\%, 0.3, \frac{2}{5}
Explanation: To compare the numbers, convert them to the same format, such as decimals. 0.30.3 is already a decimal. 35%35\% is equal to 0.350.35. 25\frac{2}{5} is equal to 0.40.4. The numbers in decimal form are 0.30.3, 0.350.35, and 0.40.4. Arranging these from least to greatest gives 0.30.3, 0.350.35, 0.40.4, which corresponds to the original list 0.3,35%,250.3, 35\%, \frac{2}{5}.

Question 13

Which of the following numbers has the greatest value?

  1. 35\frac{3}{5}
  2. 60.5%
  3. 0.62
  4. 58\frac{5}{8} (correct answer)
Explanation: To find the greatest value, convert all numbers to decimals. A: 35=0.60\frac{3}{5} = 0.60. B: 60.5%=0.60560.5\% = 0.605. C: 0.620.62. D: 58=0.625\frac{5}{8} = 0.625. Comparing the decimals 0.600.60, 0.6050.605, 0.620.62, and 0.6250.625, the greatest value is 0.6250.625, which corresponds to 58\frac{5}{8}.

Question 14

A calculation is performed: 0.5180.5 - \frac{1}{8}. Which of the following is equivalent to the result?

  1. 3.75%
  2. 14\frac{1}{4}
  3. 37%
  4. 38\frac{3}{8} (correct answer)
Explanation: First, perform the calculation. It's easiest to convert both numbers to decimals. 18=0.125\frac{1}{8} = 0.125. So, the calculation is 0.50.125=0.3750.5 - 0.125 = 0.375. Now, find which answer choice is equivalent to 0.3750.375. A: 3.75%=0.03753.75\% = 0.0375. B: 14=0.25\frac{1}{4} = 0.25. C: 37%=0.3737\% = 0.37. D: 38=3÷8=0.375\frac{3}{8} = 3 \div 8 = 0.375. The correct equivalent value is 38\frac{3}{8}.

Question 15

Three of the following values are equivalent. Which value is NOT equivalent to the others?

  1. 0.625
  2. 58\frac{5}{8}
  3. 62.5%
  4. 610\frac{6}{10} (correct answer)
Explanation: To find the value that is not equivalent, convert all options to a common format, such as a decimal. 0.6250.625 is already a decimal. 58=5÷8=0.625\frac{5}{8} = 5 \div 8 = 0.625. 62.5%=62.5÷100=0.62562.5\% = 62.5 \div 100 = 0.625. 610=0.6\frac{6}{10} = 0.6. The values 0.6250.625, 58\frac{5}{8}, and 62.5%62.5\% are all equivalent. The value 610\frac{6}{10} is different.

Question 16

A value is calculated by taking 25% of 3. Which of the following is greater than this value?

  1. 35\frac{3}{5}
  2. 0.7
  3. 72%
  4. 45\frac{4}{5} (correct answer)
Explanation: First, calculate the value: 25% of 3 is 0.25×3=0.750.25 \times 3 = 0.75. Next, compare this value to the answer choices by converting them to decimals. A: 35=0.6\frac{3}{5} = 0.6. B: 0.70.7. C: 72%=0.7272\% = 0.72. D: 45=0.8\frac{4}{5} = 0.8. We are looking for a value greater than 0.750.75. Only 0.80.8 is greater than 0.750.75.

Question 17

Which of the following inequalities is true?

  1. 34<0.8-\frac{3}{4} < -0.8
  2. 23<0.7-\frac{2}{3} < -0.7
  3. 0.6>12-0.6 > -\frac{1}{2}
  4. 0.7>45-0.7 > -\frac{4}{5} (correct answer)
Explanation: Convert fractions to decimals to compare. A: 34=0.75-\frac{3}{4} = -0.75. Is 0.75<0.8-0.75 < -0.8? False. B: 230.667-\frac{2}{3} \approx -0.667. Is 0.667<0.7-0.667 < -0.7? False. C: 12=0.5-\frac{1}{2} = -0.5. Is 0.6>0.5-0.6 > -0.5? False. For negative numbers, the number with the smaller absolute value is greater. D: 45=0.8-\frac{4}{5} = -0.8. Is 0.7>0.8-0.7 > -0.8? True. On a number line, -0.7 is to the right of -0.8.

Question 18

The length of a part must be between 0.45 inches and 12\frac{1}{2} inch. Which of the following lengths is NOT an acceptable length?

  1. 1125\frac{11}{25} inches (correct answer)
  2. 0.46 inches
  3. 1940\frac{19}{40} inches
  4. 0.49 inches
Explanation: First, define the acceptable range in a consistent format, like decimals. The range is between 0.45 inches and 12=0.5\frac{1}{2} = 0.5 inches. Now check each option. A: 1125=0.44\frac{11}{25} = 0.44 inches. This is less than 0.45, so it is outside the acceptable range. B: 0.46 is between 0.45 and 0.5. C: 1940=0.475\frac{19}{40} = 0.475 is between 0.45 and 0.5. D: 0.49 is between 0.45 and 0.5. Therefore, 1125\frac{11}{25} inches is not an acceptable length.

Question 19

A certain length is 20% of 32\frac{3}{2} meters. Which of the following lengths is shorter than this length?

  1. 14\frac{1}{4} meter (correct answer)
  2. 13\frac{1}{3} meter
  3. 0.35 meters
  4. 40% of a meter
Explanation: First, calculate the length. 32\frac{3}{2} meters is 1.5 meters. 20% of 1.5 meters is 0.20×1.5=0.30.20 \times 1.5 = 0.3 meters. The question asks which option is shorter than 0.3 meters. Convert the options to decimals: A: 14=0.25\frac{1}{4} = 0.25. B: 130.333...\frac{1}{3} \approx 0.333.... C: 0.350.35. D: 40%40\% of a meter is 0.40.4 meters. Comparing these, only 0.250.25 is shorter than 0.30.3.

Question 20

Over one year, the value of Stock X increased by 110\frac{1}{10}. The value of Stock Y increased by 9.5%. The value of Stock Z increased by 0.105. Which stock had the greatest increase in value?

  1. Stock X
  2. Stock Y
  3. Stock Z (correct answer)
  4. All stocks had the same increase.
Explanation: To compare the increases, convert them all to the same format, such as a decimal or a percent. Stock X: 110=0.10=10%\frac{1}{10} = 0.10 = 10\%. Stock Y: 9.5%=0.0959.5\% = 0.095. Stock Z: 0.105=10.5%0.105 = 10.5\%. Comparing the percentages 10%10\%, 9.5%9.5\%, and 10.5%10.5\%, the greatest value is 10.5%10.5\%, which corresponds to Stock Z.