ACCUPLACER Arithmetic Quiz: Converting Decimals And Fractions
20 questions · exam conditions
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Converting Decimals And FractionsQuestion 1 of 20

What is the value of the expression (15+0.4)×12(\frac{1}{5} + 0.4) \times \frac{1}{2}?

0.225
0.25
0.3
0.4
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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Converting Decimals And Fractions

Practice Converting Decimals And Fractions 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 Converting Decimals And Fractions, 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

What is the value of the expression (15+0.4)×12(\frac{1}{5} + 0.4) \times \frac{1}{2}?

  1. 0.225
  2. 0.25
  3. 0.3 (correct answer)
  4. 0.4
Explanation: First, evaluate the expression inside the parentheses. Convert 15\frac{1}{5} to a decimal, which is 0.2. Then, add: 0.2+0.4=0.60.2 + 0.4 = 0.6. Next, multiply the result by 12\frac{1}{2}, which is the same as multiplying by 0.5. 0.6×0.5=0.30.6 \times 0.5 = 0.3.

Question 2

Which of the following numbers has a value between 25\frac{2}{5} and 12\frac{1}{2}?

  1. 0.45 (correct answer)
  2. 0.39
  3. 38\frac{3}{8}
  4. 59\frac{5}{9}
Explanation: To compare the numbers, convert the fractions to decimals. 25=0.4\frac{2}{5} = 0.4 and 12=0.5\frac{1}{2} = 0.5. The question asks for a number between 0.4 and 0.5. The number 0.45 is between 0.4 and 0.5. The other options are 38=0.375\frac{3}{8} = 0.375 (too small), 0.39 (too small), and 59≈0.556\frac{5}{9} \approx 0.556 (too large).

Question 3

A list of numbers is shown: 58,0.6,23,0.65\frac{5}{8}, 0.6, \frac{2}{3}, 0.65. Which number is the second smallest in the list?

  1. 0.6
  2. 58\frac{5}{8} (correct answer)
  3. 0.65
  4. 23\frac{2}{3}
Explanation: To order the numbers, convert them all to decimals with the same number of places. 58=0.625\frac{5}{8} = 0.625, 0.6=0.6000.6 = 0.600, 23≈0.667\frac{2}{3} \approx 0.667, and 0.65=0.6500.65 = 0.650. Ordering from least to greatest gives: 0.600, 0.625, 0.650, 0.667. The corresponding original numbers are 0.6, 58\frac{5}{8}, 0.65, 23\frac{2}{3}. The second smallest number is 58\frac{5}{8}.

Question 4

A piece of lumber is 4.8 meters long. A carpenter cuts off a piece that is 2142 \frac{1}{4} meters long. What is the length, in meters, of the remaining piece of lumber?

  1. 2.3
  2. 2.55 (correct answer)
  3. 2.65
  4. 7.05
Explanation: First, convert the mixed number 2142 \frac{1}{4} to a decimal. 14\frac{1}{4} is 0.25, so 2142 \frac{1}{4} is 2.25. To find the length of the remaining piece, subtract the length of the cut piece from the original length: 4.8−2.254.8 - 2.25. Aligning the decimals gives 4.80−2.25=2.554.80 - 2.25 = 2.55. The remaining piece is 2.55 meters long.

Question 5

What is the result of 32×0.2\frac{3}{2} \times 0.2?

  1. 320\frac{3}{20}
  2. 152\frac{15}{2}
  3. 34\frac{3}{4}
  4. 310\frac{3}{10} (correct answer)
Explanation: To solve this, you can convert both numbers to the same format. As fractions: 0.2=210=150.2 = \frac{2}{10} = \frac{1}{5}. Then multiply: 32×15=3×12×5=310\frac{3}{2} \times \frac{1}{5} = \frac{3 \times 1}{2 \times 5} = \frac{3}{10}. Alternatively, as decimals: 32=1.5\frac{3}{2} = 1.5. Then multiply: 1.5×0.2=0.31.5 \times 0.2 = 0.3. The fraction 310\frac{3}{10} is equivalent to the decimal 0.3.

Question 6

What is the difference between 2382 \frac{3}{8} and 2.3?

  1. 0.05
  2. 0.075 (correct answer)
  3. 0.125
  4. 0.75
Explanation: First, convert the mixed number 2382 \frac{3}{8} to a decimal. Since 18=0.125\frac{1}{8} = 0.125, then 38=3×0.125=0.375\frac{3}{8} = 3 \times 0.125 = 0.375. So, 238=2.3752 \frac{3}{8} = 2.375. The difference is found by subtracting the smaller number from the larger number: 2.375−2.300=0.0752.375 - 2.300 = 0.075.

Question 7

A recipe calls for 94\frac{9}{4} cups of sugar. Which of the following decimal measurements is the same amount?

  1. 1.8
  2. 2.25 (correct answer)
  3. 2.5
  4. 4.5
Explanation: To convert the improper fraction 94\frac{9}{4} to a decimal, divide the numerator (9) by the denominator (4). 9÷4=2.259 \div 4 = 2.25. Alternatively, convert it to a mixed number: 94=214\frac{9}{4} = 2 \frac{1}{4}. Since 14=0.25\frac{1}{4} = 0.25, the decimal is 2.25.

Question 8

What is the product of 0.6 and 58\frac{5}{8}?

  1. 38\frac{3}{8} (correct answer)
  2. 12\frac{1}{2}
  3. 35\frac{3}{5}
  4. 154\frac{15}{4}
Explanation: To find the product, convert the decimal to a fraction. 0.6=610=350.6 = \frac{6}{10} = \frac{3}{5}. Now multiply the fractions: 35×58\frac{3}{5} \times \frac{5}{8}. The 5s in the numerator and denominator cancel out, leaving 38\frac{3}{8}. Alternatively, convert 58\frac{5}{8} to 0.625 and multiply 0.6×0.625=0.3750.6 \times 0.625 = 0.375, which is equal to 38\frac{3}{8}.

Question 9

A point is exactly halfway between 0.2 and 35\frac{3}{5} on a number line. What is the value of the point?

  1. 0.35
  2. 0.4 (correct answer)
  3. 0.45
  4. 0.8
Explanation: First, convert 35\frac{3}{5} to a decimal: 3÷5=0.63 \div 5 = 0.6. To find the point halfway between 0.2 and 0.6, find their average. Add the two numbers and divide by 2: (0.2+0.6)÷2=0.8÷2=0.4(0.2 + 0.6) \div 2 = 0.8 \div 2 = 0.4.

Question 10

Which of the following fractions is closest in value to 0.58?

  1. 12\frac{1}{2}
  2. 58\frac{5}{8}
  3. 35\frac{3}{5}
  4. 47\frac{4}{7} (correct answer)
Explanation: To find the closest fraction, convert each fraction to a decimal and compare its distance from 0.58. 12=0.50\frac{1}{2} = 0.50, which is 0.58−0.50=0.080.58 - 0.50 = 0.08 away. 47≈0.571\frac{4}{7} \approx 0.571, which is 0.58−0.571=0.0090.58 - 0.571 = 0.009 away. 35=0.60\frac{3}{5} = 0.60, which is 0.60−0.58=0.020.60 - 0.58 = 0.02 away. 58=0.625\frac{5}{8} = 0.625, which is 0.625−0.58=0.0450.625 - 0.58 = 0.045 away. The smallest difference is 0.009, so 47\frac{4}{7} is the closest.

Question 11

A rectangular garden is 3123 \frac{1}{2} meters long and 2.2 meters wide. What is its area in square meters, expressed as a decimal?

  1. 5.7
  2. 6.6
  3. 7.7 (correct answer)
  4. 7.8
Explanation: The area of a rectangle is length times width. First, convert the length, 3123 \frac{1}{2} meters, to a decimal, which is 3.5 meters. Then, multiply the length and width: 3.5×2.23.5 \times 2.2. The calculation is 3.5×2.2=7.73.5 \times 2.2 = 7.7. The area is 7.7 square meters.

Question 12

What is the value of 0.75+182\frac{0.75 + \frac{1}{8}}{2}, expressed as a decimal?

  1. 0.375
  2. 0.4375 (correct answer)
  3. 0.5
  4. 0.875
Explanation: First, evaluate the numerator. Convert 18\frac{1}{8} to a decimal, which is 0.125. Add the values in the numerator: 0.75+0.125=0.8750.75 + 0.125 = 0.875. Now, divide the result by 2: 0.875÷2=0.43750.875 \div 2 = 0.4375.

Question 13

What is the sum of 23\frac{2}{3} and 0.25? Express your answer as a fraction.

  1. 1112\frac{11}{12} (correct answer)
  2. 1315\frac{13}{15}
  3. 37\frac{3}{7}
  4. 2325\frac{23}{25}
Explanation: To add a fraction and a decimal, first convert the decimal to a fraction. 0.25=25100=140.25 = \frac{25}{100} = \frac{1}{4}. Now, add the two fractions: 23+14\frac{2}{3} + \frac{1}{4}. Find a common denominator, which is 12. Convert the fractions: 23=812\frac{2}{3} = \frac{8}{12} and 14=312\frac{1}{4} = \frac{3}{12}. Add them: 812+312=1112\frac{8}{12} + \frac{3}{12} = \frac{11}{12}.

Question 14

A stock is priced at \24 \frac{1}{8}$ per share. If the price increases by $1.50, what is the new price per share, expressed as a decimal?

  1. 22.625
  2. 25.275
  3. 25.625 (correct answer)
  4. 25.75
Explanation: First, convert the stock's price to a decimal. 18=0.125\frac{1}{8} = 0.125, so 241824 \frac{1}{8} is $24.125. Since the price increases, add $1.50 to this amount: 24.125+1.50=25.62524.125 + 1.50 = 25.625. The new price is $25.625.

Question 15

Which fraction is equivalent to 0.45?

  1. 49\frac{4}{9}
  2. 4510\frac{45}{10}
  3. 45\frac{4}{5}
  4. 920\frac{9}{20} (correct answer)
Explanation: To convert the decimal 0.45 to a fraction, write it as a fraction with a denominator based on its place value. The last digit is in the hundredths place, so we have 45100\frac{45}{100}. Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5. 45÷5=945 \div 5 = 9 and 100÷5=20100 \div 5 = 20. The simplified fraction is 920\frac{9}{20}.

Question 16

A measurement is recorded as 0.875 inches. Which of the following fractions, in simplest form, is equivalent to this measurement?

  1. 34\frac{3}{4}
  2. 56\frac{5}{6}
  3. 89\frac{8}{9}
  4. 78\frac{7}{8} (correct answer)
Explanation: To convert the decimal 0.875 to a fraction, write it over its place value: 8751000\frac{875}{1000}. To simplify, find the greatest common divisor of 875 and 1000. Both are divisible by 25: 875÷25=35875 \div 25 = 35 and 1000÷25=401000 \div 25 = 40, resulting in 3540\frac{35}{40}. This can be simplified further by dividing by 5: 35÷5=735 \div 5 = 7 and 40÷5=840 \div 5 = 8. The simplest form is 78\frac{7}{8}.

Question 17

What is the value of 2.5−(35×2)2.5 - (\frac{3}{5} \times 2)?

  1. 1.3 (correct answer)
  2. 1.9
  3. 3.8
  4. 4.0
Explanation: Following the order of operations, first calculate the value inside the parentheses. Convert 35\frac{3}{5} to a decimal, which is 0.6. Then multiply: 0.6×2=1.20.6 \times 2 = 1.2. Now, perform the subtraction: 2.5−1.2=1.32.5 - 1.2 = 1.3.

Question 18

Which of the following is equivalent to 716\frac{7}{16}?

  1. 0.04375
  2. 0.4275
  3. 0.4375 (correct answer)
  4. 2.2857
Explanation: To convert the fraction 716\frac{7}{16} to a decimal, divide the numerator (7) by the denominator (16). 7÷16=0.43757 \div 16 = 0.4375.

Question 19

A recipe calls for 38\frac{3}{8} cup of sugar, but Maria only has a measuring cup marked in decimal increments of 0.05 cups. What is the smallest amount she can measure that will give her at least the required amount of sugar?

  1. 0.35 cups
  2. 0.375 cups
  3. 0.38 cups
  4. 0.40 cups (correct answer)
Explanation: First convert 38\frac{3}{8} to decimal: 3÷8=0.3753 \div 8 = 0.375. Since Maria's measuring cup only measures in increments of 0.05, she needs the smallest multiple of 0.05 that is greater than or equal to 0.375. Checking: 0.35 < 0.375, so this is too little. 0.40 > 0.375, and 0.40 = 8 × 0.05, so this works. Choice A (0.35) is less than needed. Choice B (0.375) is exact but not measurable with her cup. Choice C (0.38) is not a multiple of 0.05.

Question 20

The decimal 0.64 can be written as ab\frac{a}{b} where aa and bb are positive integers with no common factors other than 1. If this same fraction ab\frac{a}{b} is used to represent a percentage, what percentage does it represent?

  1. 16%
  2. 25%
  3. 64% (correct answer)
  4. 80%
Explanation: First convert 0.64 to a fraction: 0.64=64100=16250.64 = \frac{64}{100} = \frac{16}{25} (dividing by gcd⁡(64,100)=4\gcd(64,100) = 4). So a=16a = 16 and b=25b = 25. When 1625\frac{16}{25} represents a percentage, we calculate 1625×100%=64%\frac{16}{25} \times 100\% = 64\%. Choice A would result from incorrectly using just the numerator 16. Choice B would result from calculating 25100\frac{25}{100}. Choice D would result from using 45\frac{4}{5} instead of 1625\frac{16}{25}.