SSAT Upper Level Quiz: Ordering Rational Numbers
13 questions · exam conditions
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Ordering Rational NumbersQuestion 1 of 13

Which value is between 0.44 and 4/9?

0.41
0.45
0.4448
0.4425
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SSAT Upper Level Quiz

SSAT Upper Level Quiz: Ordering Rational Numbers

Practice Ordering Rational Numbers in SSAT Upper Level 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 Ordering Rational Numbers, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Upper Level.

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

Which value is between 0.44 and 4/9?

  1. 0.41
  2. 0.45
  3. 0.4448
  4. 0.4425 (correct answer)
Explanation: Rewrite 4/9 as 0.4444..., so you need a value greater than 0.44 but less than 0.4444. Since 0.4400 < 0.4425 < 0.4444, 0.4425 fits. The tempting 0.4448 is wrong because it is greater than 0.4444..., not between them.

Question 2

Which list is ordered from least to greatest?

  1. -7/8, -3/4, -0.6, -1/2 (correct answer)
  2. -3/4, -7/8, -0.6, -1/2
  3. -1/2, -0.6, -3/4, -7/8
  4. -7/8, -0.6, -3/4, -1/2
Explanation: On the negative side, the smaller number has the larger absolute value. Since -7/8 = -0.875, -3/4 = -0.75, -0.6, and -1/2 = -0.5, the order from least to greatest is -7/8, -3/4, -0.6, -1/2. A tempting wrong answer is -1/2, -0.6, -3/4, -7/8, because that lists them from greatest to least instead.

Question 3

Which of the following is true?

  1. 3/4 < 5/8
  2. -0.7 > -1/4
  3. -2/3 < -0.5 (correct answer)
  4. 0.1 > 0.2
Explanation: Compare the values on a number line. Since -2/3 is about -0.666 and -0.5 is -0.5, -2/3 is farther left, so it is less than -0.5. The tempting wrong comparison is -0.7 > -1/4, but -0.7 is actually less than -0.25 because the farther a negative number is from zero, the smaller it is.

Question 4

Scores: 7/8, 0.82, 83%. Which shows least-to-greatest order?

  1. 0.82 < 83% < 7/8 (correct answer)
  2. 83% < 0.82 < 7/8
  3. 7/8 < 83% < 0.82
  4. 0.82 < 7/8 < 83%
Explanation: Convert each to decimals: 7/8 = 0.875, 83% = 0.83, and 0.82 stays 0.82. So from least to greatest: 0.82, 0.83, 0.875. The tempting error is putting 7/8 before 83%, but 7/8 is actually 0.875, the largest value.

Question 5

What is the least integer greater than -7/4?

  1. -2
  2. -1 (correct answer)
  3. 0
  4. 1
Explanation: Since -7/4 equals -1.75, the integers greater than it are -1, 0, 1, and so on. The least of those is -1. A common trap is choosing -2, but -2 is less than -1.75, so it is not greater than -7/4.

Question 6

In a science lab, which recorded value is the greatest: 0.620.62, 58\frac{5}{8}, 61%61\%, 0.590.59, or 35\frac{3}{5}?

  1. 0.620.62
  2. 58\frac{5}{8} (correct answer)
  3. 61%61\%
  4. 0.590.59
  5. 35\frac{3}{5}
Explanation: This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, students must identify the greatest value by converting all to decimals: 0.62 = 0.62, 5/8 = 0.625, 61% = 0.61, 0.59 = 0.59, and 3/5 = 0.60. The correct answer is choice B because 5/8 = 0.625 is the largest value among all the options. A common mistake might be choosing choice A (0.62), where students fail to recognize that 5/8 = 0.625 is actually greater than 0.62. To assist students: Encourage careful conversion of fractions to decimals and remind them that 5/8 means 5 ÷ 8. Provide practice problems that require finding the maximum or minimum value among mixed formats.

Question 7

If a=−58a = -\frac{5}{8}, b=−0.62b = -0.62, and c=−35c = -\frac{3}{5}, which of the following correctly orders these three numbers from least to greatest?

  1. a,b,ca, b, c (correct answer)
  2. a,c,ba, c, b
  3. b,a,cb, a, c
  4. b,c,ab, c, a
Explanation: First convert all numbers to decimals: a=−58=−0.625a = -\frac{5}{8} = -0.625, b=−0.62b = -0.62, and c=−35=−0.6c = -\frac{3}{5} = -0.6. Since these are all negative numbers, the number closest to zero is the greatest. Comparing: −0.625<−0.62<−0.6-0.625 < -0.62 < -0.6, so a<b<ca < b < c. Therefore, from least to greatest: a,b,ca, b, c.

Question 8

If pp and qq are integers such that pq=0.36‾\frac{p}{q} = 0.\overline{36}, what is the value of p+qp + q when the fraction is in lowest terms?

  1. 15 (correct answer)
  2. 47
  3. 51
  4. 65
Explanation: Let x=0.36‾=0.363636...x = 0.\overline{36} = 0.363636... Then 100x=36.363636...100x = 36.363636... Subtracting: 100x−x=36.363636...−0.363636...100x - x = 36.363636... - 0.363636... gives 99x=3699x = 36, so x=3699x = \frac{36}{99}. To reduce to lowest terms, find GCD(36, 99): 36=22×3236 = 2^2 \times 3^2 and 99=32×1199 = 3^2 \times 11, so GCD = 9. Therefore 3699=411\frac{36}{99} = \frac{4}{11}. Thus p=4p = 4 and q=11q = 11, so p+q=15p + q = 15.

Question 9

Three rational numbers rr, ss, and tt satisfy the following conditions: r<s<tr < s < t, r+s+t=0r + s + t = 0, and rst=18rst = \frac{1}{8}. If r=−12r = -\frac{1}{2}, which of the following represents the correct ordering of ∣r∣|r|, ∣s∣|s|, and ∣t∣|t| from least to greatest?

  1. ∣r∣,∣s∣,∣t∣|r|, |s|, |t|
  2. ∣s∣,∣r∣,∣t∣|s|, |r|, |t| (correct answer)
  3. ∣s∣,∣t∣,∣r∣|s|, |t|, |r|
  4. ∣t∣,∣s∣,∣r∣|t|, |s|, |r|
Explanation: Given r=−12r = -\frac{1}{2}, r+s+t=0r + s + t = 0, and rst=18rst = \frac{1}{8}. From r+s+t=0r + s + t = 0: s+t=−r=−(−12)=12s + t = -r = -(-\frac{1}{2}) = \frac{1}{2}. From rst=18rst = \frac{1}{8}: (−12)st=18(-\frac{1}{2})st = \frac{1}{8}, so st=−14st = -\frac{1}{4}. We have the system: s+t=12s + t = \frac{1}{2} and st=−14st = -\frac{1}{4}. These are the sum and product of roots of the quadratic x2−12x−14=0x^2 - \frac{1}{2}x - \frac{1}{4} = 0. Using the quadratic formula: x=12±14+12=12±542=12±522=1±54x = \frac{\frac{1}{2} \pm \sqrt{\frac{1}{4} + 1}}{2} = \frac{\frac{1}{2} \pm \sqrt{\frac{5}{4}}}{2} = \frac{\frac{1}{2} \pm \frac{\sqrt{5}}{2}}{2} = \frac{1 \pm \sqrt{5}}{4}. Since r<s<tr < s < t and r=−12r = -\frac{1}{2}, we need ss and tt both greater than −12-\frac{1}{2}. We have s=1−54≈1−2.2364≈−0.309s = \frac{1 - \sqrt{5}}{4} ≈ \frac{1 - 2.236}{4} ≈ -0.309 and t=1+54≈1+2.2364≈0.809t = \frac{1 + \sqrt{5}}{4} ≈ \frac{1 + 2.236}{4} ≈ 0.809. Since −12=−0.5<−0.309<0.809-\frac{1}{2} = -0.5 < -0.309 < 0.809, the ordering r<s<tr < s < t is satisfied. Now find the absolute values: ∣r∣=12=0.5|r| = \frac{1}{2} = 0.5, ∣s∣=5−14≈0.309|s| = \frac{\sqrt{5} - 1}{4} ≈ 0.309, ∣t∣=1+54≈0.809|t| = \frac{1 + \sqrt{5}}{4} ≈ 0.809. From least to greatest: ∣s∣<∣r∣<∣t∣|s| < |r| < |t|, which corresponds to choice B.

Question 10

Which of the following lists these interest rates in ascending order: 12%12\%, 0.090.09, 110\frac{1}{10}, 8%8\%, 0.110.11?

  1. 8%, 0.09, 110, 0.11, 12%8\%,\ 0.09,\ \frac{1}{10},\ 0.11,\ 12\% (correct answer)
  2. 0.09, 8%, 110, 0.11, 12%0.09,\ 8\%,\ \frac{1}{10},\ 0.11,\ 12\%
  3. 8%, 110, 0.09, 0.11, 12%8\%,\ \frac{1}{10},\ 0.09,\ 0.11,\ 12\%
  4. 12%, 0.11, 110, 0.09, 8%12\%,\ 0.11,\ \frac{1}{10},\ 0.09,\ 8\%
  5. 8%, 0.09, 0.11, 110, 12%8\%,\ 0.09,\ 0.11,\ \frac{1}{10},\ 12\%
Explanation: This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, the interest rates must be arranged in ascending order by converting all to decimals: 12% = 0.12, 0.09 = 0.09, 1/10 = 0.10, 8% = 0.08, and 0.11 = 0.11. The correct answer is choice A because it accurately represents the numbers in ascending order: 8% (0.08), 0.09, 1/10 (0.10), 0.11, 12% (0.12). A common mistake is shown in choice B, where students might incorrectly place 0.09 before 8%, not recognizing that 8% = 0.08 is smaller than 0.09. To assist students: Encourage practice with converting percentages to decimals by dividing by 100, and fractions to decimals through division. Provide exercises that mix all three formats to build confidence in ordering rational numbers.

Question 11

A sequence of rational numbers is defined by the pattern: −32,−54,−78,−916,...-\frac{3}{2}, -\frac{5}{4}, -\frac{7}{8}, -\frac{9}{16}, ... If this pattern continues, which of the following represents the correct ordering of the 6th, 7th, and 8th terms from least to greatest?

  1. 6th, 7th, 8th (correct answer)
  2. 6th, 8th, 7th
  3. 8th, 7th, 6th
  4. 7th, 8th, 6th
Explanation: First, identify the pattern. The numerators are −3,−5,−7,−9,...-3, -5, -7, -9, ... which follows −(2n+1)-(2n+1) for n=1,2,3,4,...n = 1, 2, 3, 4, ... The denominators are 2,4,8,16,...2, 4, 8, 16, ... which follows 2n2^n. So the nnth term is −2n+12n-\frac{2n+1}{2^n}. The 6th term: −1364≈−0.203-\frac{13}{64} ≈ -0.203. The 7th term: −15128≈−0.117-\frac{15}{128} ≈ -0.117. The 8th term: −17256≈−0.066-\frac{17}{256} ≈ -0.066. Since −0.203<−0.117<−0.066-0.203 < -0.117 < -0.066, we have 6th < 7th < 8th. Therefore, from least to greatest: 6th, 7th, 8th.

Question 12

At a store, rank these discounts from smallest to largest value: 15\frac{1}{5}, 0.180.18, 15%15\%, 316\frac{3}{16}, 0.220.22.

  1. 15%, 15, 0.18, 316, 0.2215\%,\ \frac{1}{5},\ 0.18,\ \frac{3}{16},\ 0.22
  2. 15%, 0.18, 316, 15, 0.2215\%,\ 0.18,\ \frac{3}{16},\ \frac{1}{5},\ 0.22 (correct answer)
  3. 0.18, 15%, 316, 15, 0.220.18,\ 15\%,\ \frac{3}{16},\ \frac{1}{5},\ 0.22
  4. 15%, 0.18, 15, 316, 0.2215\%,\ 0.18,\ \frac{1}{5},\ \frac{3}{16},\ 0.22
  5. 15%, 0.18, 316, 0.22, 1515\%,\ 0.18,\ \frac{3}{16},\ 0.22,\ \frac{1}{5}
Explanation: This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, the discounts must be arranged from smallest to largest by converting all values to decimals: 15% = 0.15, 1/5 = 0.20, 0.18 = 0.18, 3/16 = 0.1875, and 0.22 = 0.22. The correct answer is choice B because it accurately represents the numbers in the correct order: 15% (0.15), 0.18, 3/16 (0.1875), 1/5 (0.20), 0.22. A common mistake is shown in choice A, where students might place 1/5 before 3/16, not realizing that 1/5 = 0.20 is greater than 3/16 = 0.1875. To assist students: Encourage practice with converting between formats and stress the importance of attention to detail with decimal placement. Provide exercises that involve ordering mixed formats to develop flexibility in working with percentages, fractions, and decimals.

Question 13

A science experiment lists solution concentrations: 0.1250.125, 110\frac{1}{10}, 13%13\%, 0.120.12, 325\frac{3}{25}. Which is greatest?

  1. 110\frac{1}{10}
  2. 0.1250.125
  3. 13%13\% (correct answer)
  4. 0.120.12
  5. 325\frac{3}{25}
Explanation: This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, students must identify the greatest concentration by converting all to decimals: 0.125 = 0.125, 1/10 = 0.10, 13% = 0.13, 0.12 = 0.12, and 3/25 = 0.12. The correct answer is choice C because 13% = 0.13 is the largest value among all the options. A common mistake might be choosing choice B (0.125), where students might think the number with more decimal places is larger, not recognizing that 0.13 > 0.125. To assist students: Emphasize place value understanding and that 0.13 = 0.130 when comparing decimals. Provide exercises focusing on decimal comparison with different numbers of decimal places.