ACCUPLACER Arithmetic Quiz: Comparing And Ordering Decimals
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Comparing And Ordering DecimalsQuestion 1 of 20

A lab technician measures liquid volumes: 15.615.6 mL, 15.0615.06 mL, 15.00615.006 mL, and 15.6615.66 mL. Which two volumes have the greatest difference between them?

15.615.6 mL and 15.00615.006 mL
15.615.6 mL and 15.0615.06 mL
15.6615.66 mL and 15.0615.06 mL
15.6615.66 mL and 15.00615.006 mL
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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Comparing And Ordering Decimals

Practice Comparing And Ordering Decimals 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 And Ordering Decimals, 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

A lab technician measures liquid volumes: 15.615.6 mL, 15.0615.06 mL, 15.00615.006 mL, and 15.6615.66 mL. Which two volumes have the greatest difference between them?

  1. 15.615.6 mL and 15.00615.006 mL
  2. 15.615.6 mL and 15.0615.06 mL
  3. 15.6615.66 mL and 15.0615.06 mL
  4. 15.6615.66 mL and 15.00615.006 mL (correct answer)
Explanation: When comparing decimal numbers, you need to carefully examine each digit's place value to determine which numbers are furthest apart. The key is to align the decimal places and subtract to find the actual differences. Let's find the difference for each pair. First, organize the numbers by size: 15.00615.006 (smallest), 15.0615.06, 15.615.6, and 15.6615.66 (largest). The greatest difference will be between the largest and smallest values: 15.66−15.006=0.65415.66 - 15.006 = 0.654 mL. Let's verify by checking the other options. Option A gives us 15.6−15.006=0.59415.6 - 15.006 = 0.594 mL. Option B yields 15.6−15.06=0.5415.6 - 15.06 = 0.54 mL. Option C produces 15.66−15.06=0.615.66 - 15.06 = 0.6 mL. Comparing all differences, 0.6540.654 mL is indeed the largest, confirming that option D is correct. Option A is wrong because while 15.615.6 and 15.00615.006 are far apart, 15.6615.66 is even larger than 15.615.6, creating a greater gap. Option B is incorrect because both numbers are relatively close to each other in the middle range. Option C fails because although 15.6615.66 is the largest number, 15.0615.06 isn't the smallest—15.00615.006 is smaller. When finding the greatest difference between numbers in a set, always identify the maximum and minimum values first. This saves time and prevents calculation errors. Also, be extra careful with decimal place values—15.0615.06 and 15.00615.006 look similar but differ significantly in the hundredths place.

Question 2

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

  1. -1.5, -1.05, -1.45, -1.04
  2. -1.5, -1.45, -1.05, -1.04 (correct answer)
  3. -1.04, -1.05, -1.45, -1.5
  4. -1.45, -1.5, -1.04, -1.05
Explanation: When ordering negative numbers, the number with the largest absolute value is the least. Comparing the numbers: -1.5 is the smallest. Then comes -1.45. Next is -1.05. The greatest number is -1.04. The correct order from least to greatest is -1.5, -1.45, -1.05, -1.04.

Question 3

Which of the following values is closest to 0.6?

  1. 0.59
  2. 0.601 (correct answer)
  3. 0.598
  4. 0.61
Explanation: To find the value closest to 0.6, calculate the absolute difference between 0.6 and each option: |0.6 - 0.59| = 0.01; |0.6 - 0.601| = 0.001; |0.6 - 0.598| = 0.002; |0.6 - 0.61| = 0.01. The smallest difference is 0.001, which corresponds to the value 0.601.

Question 4

What is the result when the numbers -2.1, 1.2, -1.2, and 2.01 are arranged in order from least to greatest?

  1. -2.1, -1.2, 1.2, 2.01 (correct answer)
  2. -1.2, -2.1, 1.2, 2.01
  3. 2.01, 1.2, -1.2, -2.1
  4. -2.1, -1.2, 2.01, 1.2
Explanation: To order from least to greatest, start with the most negative number. -2.1 is less than -1.2. Then order the positive numbers. 1.2 is less than 2.01. The complete order is -2.1, -1.2, 1.2, 2.01.

Question 5

Three of the following numbers are between 3.1 and 3.2. Which number is NOT in this range?

  1. 3.105
  2. 3.15
  3. 3.099 (correct answer)
  4. 3.199
Explanation: A number between 3.1 and 3.2 must be greater than 3.1 and less than 3.2. A) 3.105 is in the range. B) 3.15 is in the range. C) 3.099 is less than 3.1, so it is not in the range. D) 3.199 is in the range. The number not in the range is 3.099.

Question 6

A baker adds 0.375 pounds of flour to a recipe. He needs to add another ingredient that weighs more than the flour. Which of the following weights is greater than 0.375 pounds?

  1. 3/8 pounds
  2. 1/3 pounds
  3. 2/5 pounds (correct answer)
  4. 3/10 pounds
Explanation: First, convert the fractions to decimals to compare them with 0.375. A) 3/8 = 0.375. This is equal, not greater. B) 1/3 ≈ 0.333. This is less than 0.375. C) 2/5 = 0.4. This is greater than 0.375. D) 3/10 = 0.3. This is less than 0.375. The only weight greater than 0.375 pounds is 2/5 pounds.

Question 7

On a number line, which of the following values is located to the right of -4.6 but to the left of -4.5?

  1. -4.65
  2. -4.55 (correct answer)
  3. -4.7
  4. -4.4
Explanation: On a number line, 'to the right' means greater than, and 'to the left' means less than. The question is asking for a number x such that -4.6 < x < -4.5. A) -4.65 is less than -4.6. B) -4.55 is greater than -4.6 and less than -4.5. C) -4.7 is less than -4.6. D) -4.4 is greater than -4.5. The correct value is -4.55.

Question 8

A bank offers four different savings accounts with the following annual interest rates: 0.02, 0.015, 0.021, and 0.019. To earn the most interest, which rate should a customer choose?

  1. 0.015
  2. 0.019
  3. 0.02
  4. 0.021 (correct answer)
Explanation: To earn the most interest, the customer should choose the account with the highest interest rate. Comparing the decimal values: 0.015, 0.019, 0.020 (same as 0.02), and 0.021. The largest of these numbers is 0.021.

Question 9

A number is formed by placing a digit from 1 to 9 in the blank: 5.1_8. Which digit in the blank would make this number greater than 5.178 but less than 5.198?

  1. 6
  2. 7
  3. 8 (correct answer)
  4. 9
Explanation: The number must satisfy the inequality 5.178 < 5.1_8 < 5.198. Let's test the options: A) 5.168 is not greater than 5.178. B) 5.178 is not strictly greater than 5.178. C) 5.188 is greater than 5.178 and less than 5.198. D) 5.198 is not strictly less than 5.198. The only digit that works is 8.

Question 10

Consider two calculations: Calculation P: 2.5 - 0.05 Calculation Q: 2.4 + 0.055 Which of the following statements correctly compares the results?

  1. The result of P is less than the result of Q. (correct answer)
  2. The result of P is equal to the result of Q.
  3. The result of P is greater than the result of Q.
  4. The comparison cannot be made without a calculator.
Explanation: First, perform each calculation. Calculation P: 2.5 - 0.05 = 2.45. Calculation Q: 2.4 + 0.055 = 2.455. Next, compare the two results: 2.45 and 2.455. Since 2.450 is less than 2.455, the result of P is less than the result of Q.

Question 11

A delivery service sorts packages by weight. Package weights are 3.083.08 kg, 3.0083.008 kg, 3.83.8 kg, and 3.0803.080 kg. How many packages weigh more than 3.073.07 kg but less than 3.13.1 kg?

  1. 1
  2. 2 (correct answer)
  3. 3
  4. 4
Explanation: We need weights where 3.07 < weight < 3.1. Checking each: 3.08 kg (yes, 3.07 < 3.08 < 3.1), 3.008 kg (no, 3.008 < 3.07), 3.8 kg (no, 3.8 > 3.1), 3.080 kg (yes, same as 3.08, so 3.07 < 3.08 < 3.1). Two packages meet the criteria. Other choices miscount the packages in the specified range.

Question 12

A pharmacist needs to measure a liquid medicine dose that is greater than 1.25 mL but less than 1.3 mL. Which of the following doses is acceptable?

  1. 1.248 mL
  2. 1.25 mL
  3. 1.28 mL (correct answer)
  4. 1.3 mL
Explanation: The question asks for a number between 1.25 and 1.3. A) 1.248 is less than 1.25. B) 1.25 is not greater than 1.25. C) 1.28 is greater than 1.25 and less than 1.3. D) 1.3 is not less than 1.3. Therefore, 1.28 mL is the only acceptable dose.

Question 13

Four runners competed in a 100-meter dash. Their times were 10.3 seconds, 10.03 seconds, 10.13 seconds, and 10.31 seconds. In racing, the shortest time wins. Which time earned the silver medal (second place)?

  1. 10.03 seconds
  2. 10.13 seconds (correct answer)
  3. 10.3 seconds
  4. 10.31 seconds
Explanation: To find the second-place time, the times must be ordered from least (fastest) to greatest (slowest). The correct order is: 10.03 (first place), 10.13 (second place), 10.3 (third place), and 10.31 (fourth place). The time that earned the silver medal is the second-fastest time, which is 10.13 seconds.

Question 14

Three runners complete a race with times of 12.04512.045 seconds, 12.412.4 seconds, and 12.0512.05 seconds. A fourth runner's time is greater than the fastest time but less than 12.04612.046 seconds. Which decimal could represent the fourth runner's time?

  1. 12.045112.0451 (correct answer)
  2. 12.04412.044
  3. 12.045912.0459
  4. 12.04612.046
Explanation: The fastest time is 12.045 seconds. The fourth runner's time must be between 12.045 and 12.046 (exclusive). Only 12.0451 satisfies 12.045 < 12.0451 < 12.046. Choice B (12.044) is less than 12.045. Choice C (12.0459) is greater than 12.046. Choice D (12.046) equals the upper bound, not less than it.

Question 15

A machinist measures bolt diameters: 0.2490.249 inches, 0.250.25 inches, 0.24950.2495 inches, and 0.25050.2505 inches. Bolts with diameters between 0.2480.248 and 0.2510.251 inches (inclusive) pass inspection. Which statement about the inspection results is correct?

  1. Exactly three bolts pass inspection
  2. All four bolts pass inspection (correct answer)
  3. Only two bolts pass inspection
  4. Just one bolt passes inspection
Explanation: Checking each diameter against 0.248 ≤ diameter ≤ 0.251: 0.249 (passes), 0.25 (passes), 0.2495 (passes), 0.2505 (passes). All measurements fall within the acceptable range. Choice A undercounts by one. Choices C and D significantly undercount the passing bolts.

Question 16

A pharmacist needs to dispense medication doses in ascending order. The prescribed doses are 2.752.75 mg, 2.7052.705 mg, 2.72.7 mg, and 2.7152.715 mg. After arranging them correctly, which dose comes third in the sequence?

  1. 2.72.7 mg
  2. 2.7052.705 mg
  3. 2.7152.715 mg (correct answer)
  4. 2.752.75 mg
Explanation: Converting to thousandths: 2.700, 2.705, 2.715, 2.750. In ascending order: 2.7, 2.705, 2.715, 2.75. The third position is 2.715 mg. Choice A (2.7) is first. Choice B (2.705) is second. Choice D (2.75) is fourth in the sequence.

Question 17

A baker weighs ingredients: flour at 1.2051.205 pounds, sugar at 1.251.25 pounds, butter at 1.21.2 pounds, and salt at 1.2151.215 pounds. If ingredients must be added in order from lightest to heaviest, which ingredient should be added second?

  1. Salt at 1.2151.215 pounds
  2. Sugar at 1.251.25 pounds
  3. Butter at 1.21.2 pounds
  4. Flour at 1.2051.205 pounds (correct answer)
Explanation: When comparing decimal numbers, you need to align the decimal places and compare digit by digit from left to right. This question tests your ability to order decimals from smallest to largest. Let's arrange all the weights with the same number of decimal places to make comparison easier: flour (1.2051.205), sugar (1.2501.250), butter (1.2001.200), and salt (1.2151.215). Since all weights start with 1.21.2, we need to look at the hundredths and thousandths places to determine the order. Comparing the digits after 1.21.2: butter has 0000 (1.2001.200), flour has 0505 (1.2051.205), salt has 1515 (1.2151.215), and sugar has 5050 (1.2501.250). This gives us the order from lightest to heaviest: butter (1.21.2), flour (1.2051.205), salt (1.2151.215), sugar (1.251.25). The second ingredient to be added is flour at 1.2051.205 pounds. Looking at the wrong answers: A) Salt at 1.2151.215 pounds is the third heaviest, not second lightest. B) Sugar at 1.251.25 pounds is actually the heaviest ingredient, so it would be added last. C) Butter at 1.21.2 pounds is the lightest ingredient, so it would be added first, not second. When ordering decimals, write them with the same number of decimal places by adding zeros as needed. This makes it much easier to compare values and avoid mistakes with numbers that look similar but have different place values.

Question 18

A quality control inspector measures the thickness of metal sheets. The measurements are: 0.06250.0625 inches, 0.0630.063 inches, 0.06190.0619 inches, and 0.062050.06205 inches. If the sheets must be arranged from thinnest to thickest for packaging, what is the correct order?

  1. 0.06190.0619, 0.062050.06205, 0.06250.0625, 0.0630.063 (correct answer)
  2. 0.06190.0619, 0.06250.0625, 0.062050.06205, 0.0630.063
  3. 0.062050.06205, 0.06190.0619, 0.06250.0625, 0.0630.063
  4. 0.0630.063, 0.06250.0625, 0.062050.06205, 0.06190.0619
Explanation: To compare decimals, align decimal places: 0.0619 < 0.06205 < 0.0625 < 0.063. Choice A correctly orders from thinnest to thickest. Choice B incorrectly places 0.0625 before 0.06205. Choice C incorrectly places 0.06205 before 0.0619. Choice D orders from thickest to thinnest instead of thinnest to thickest.

Question 19

A mechanic is checking the gap of a spark plug. The acceptable range is from 0.7 millimeters to 0.8 millimeters, inclusive. Which of the following measurements is too small?

  1. 0.701 mm
  2. 0.79 mm
  3. 0.8 mm
  4. 0.695 mm (correct answer)
Explanation: The acceptable range is [0.7, 0.8]. A measurement is 'too small' if it is less than 0.7. A) 0.701 is in the range. B) 0.79 is in the range. C) 0.8 is the maximum acceptable value, not too small. D) 0.695 is less than 0.7, so it is too small.

Question 20

Which of the following statements is true?

  1. 0.45 < 2/5
  2. 0.7 > 3/4
  3. 0.125 = 1/8 (correct answer)
  4. 0.6 > 2/3
Explanation: To evaluate each statement, convert the fractions to decimals. A) 2/5 = 0.4. The statement 0.45 < 0.4 is false. B) 3/4 = 0.75. The statement 0.7 > 0.75 is false. C) 1/8 = 0.125. The statement 0.125 = 0.125 is true. D) 2/3 = 0.666... The statement 0.6 > 0.666... is false.