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Quizzes > High School Quizzes > Mathematics

Ordering Real Numbers Practice Quiz

Strengthen real number ordering with engaging exercises

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Rank the Reals, a high school math quiz about arranging real numbers.

Which number is the smallest: 0.2, 0.5, 0.7, or 0.9?
0.7
0.5
0.9
0.2
0.2 is clearly the smallest value because it is lower than the other options. This fundamental comparison builds confidence in ordering real numbers.
Which of the following is the correct ascending order for the numbers: -3, 0, 2, and 5?
0, -3, 2, 5
5, 2, 0, -3
2, 0, -3, 5
-3, 0, 2, 5
The numbers arranged from the smallest to the largest are -3, 0, 2, and 5. This question reinforces basic integer ordering.
Which number is greater: -2 or -1.5?
It cannot be determined
They are equal
-1.5
-2
On the number line, -1.5 is to the right of -2, making it the greater number. Understanding negative values is essential in ordering real numbers.
Which of the following numbers is the largest: 1/4, 0.20, 0.3, or 1/3?
1/3
0.20
0.3
1/4
When converted to decimals, 1/4 equals 0.25 and 1/3 is approximately 0.333. Thus, 1/3 is the largest number among the options.
Place the following numbers in ascending order: 0, -1, 1, and -2.
-2, 0, -1, 1
0, -2, -1, 1
-2, -1, 0, 1
-1, -2, 0, 1
Ordering these values from smallest to largest gives -2, then -1, followed by 0, and finally 1. This reinforces the concept of ordering both negative and positive numbers.
Which sequence correctly orders the numbers 0.9, 1, 1.1, and 1.01 in ascending order?
1.1, 1.01, 1, 0.9
0.9, 1, 1.01, 1.1
0.9, 1, 1.1, 1.01
1, 0.9, 1.01, 1.1
In this set, 0.9 is the smallest, followed by 1, then 1.01, and finally 1.1. Recognizing the significance of decimal place value is key to ordering accurately.
Arrange the following numbers in increasing order: √2, 1.5, 2, and π.
1.5, √2, 2, π
√2, 1.5, 2, π
π, 2, 1.5, √2
1.5, 2, √2, π
With √2 approximating 1.414 and π nearly 3.14, the ascending order is √2, then 1.5, followed by 2, and finally π. This question challenges you to compare irrational numbers with decimals.
Which of the following is the correct ascending order for the numbers: -√2, -1, -1/2, and 0?
0, -1/2, -1, -√2
-1/2, -1, -√2, 0
-1, -√2, -1/2, 0
-√2, -1, -1/2, 0
Since -√2 is approximately -1.414, it is the smallest number, followed by -1, then -0.5 (which is -1/2), and finally 0. This reinforces handling of negative numbers and radicals in order.
Arrange the following numbers in increasing order: 2/3, 0.67, 0.666, and 0.7.
2/3, 0.666, 0.67, 0.7
0.666, 0.67, 2/3, 0.7
0.67, 0.666, 2/3, 0.7
0.666, 2/3, 0.67, 0.7
Here, 2/3 is approximately 0.6667, which is just above 0.666; 0.67 comes next, and 0.7 is the largest. Attention to detail with decimal values is crucial in such comparisons.
Which sequence correctly lists the numbers 3.25, 3.2, 3.15, and 3.1 in descending order?
3.25, 3.2, 3.15, 3.1
3.1, 3.15, 3.2, 3.25
3.2, 3.25, 3.15, 3.1
3.25, 3.15, 3.2, 3.1
Descending order arranges numbers from the highest to the lowest. Since 3.25 is the largest and 3.1 the smallest, option A is correct.
Arrange the following numbers in increasing order: 7/8, 0.88, 0.87, and 0.9.
0.87, 7/8, 0.88, 0.9
0.9, 0.88, 7/8, 0.87
0.87, 0.88, 7/8, 0.9
7/8, 0.87, 0.9, 0.88
Converting 7/8 to decimal gives 0.875, which lies between 0.87 and 0.88. Therefore, the correct order is 0.87, then 7/8, followed by 0.88, and finally 0.9.
In which order do the following numbers appear from smallest to largest: √3, 1.7, 1.73, and 1.74?
1.7, 1.73, 1.74, √3
1.7, 1.73, √3, 1.74
√3, 1.7, 1.73, 1.74
1.7, √3, 1.73, 1.74
Since √3 is approximately 1.732, it falls between 1.73 and 1.74. Thus, the ascending order is 1.7, then 1.73, followed by √3, and finally 1.74.
Determine the correct ascending order for these negative decimals: -0.3, -0.33, -0.25, and -0.35.
-0.35, -0.33, -0.3, -0.25
-0.33, -0.35, -0.3, -0.25
-0.3, -0.25, -0.33, -0.35
-0.25, -0.3, -0.33, -0.35
Among negative numbers, the one with the highest absolute value is the smallest. Thus, -0.35 comes first, followed by -0.33, then -0.3, with -0.25 being the largest.
Arrange these numbers in ascending order: 3/2, 1.4, √2, and 1.5.
1.4, 1.5, √2, 3/2
1.5, 3/2, √2, 1.4
1.4, √2, 1.5, 3/2
√2, 1.4, 3/2, 1.5
Since 3/2 and 1.5 are equivalent and √2 is approximately 1.414, the correct order is 1.4, then √2, followed by 1.5 (or 3/2). This question tests your ability to compare fractions, decimals, and irrational numbers.
Arrange the following numbers in increasing order: -π, -3.2, -3.1, and -3.
-π, -3.2, -3.1, -3
-3.2, -π, -3.1, -3
-3.2, -3.1, -π, -3
-3, -3.1, -π, -3.2
Taking π as approximately 3.14, -π is about -3.14. Thus, the order from smallest to largest is -3.2, then -π, followed by -3.1, and -3 is the largest among the negatives.
Determine the correct ascending order for the following expressions: 1.4, √2, 1.4 + 0.2, and 0.2 + √2.
1.4, √2, 1.4 + 0.2, 0.2 + √2
1.4, 1.4 + 0.2, √2, 0.2 + √2
√2, 1.4, 1.4 + 0.2, 0.2 + √2
√2, 1.4, 0.2 + √2, 1.4 + 0.2
Approximating √2 to about 1.414, we have 1.4, then roughly 1.414, then 1.4 + 0.2 which is 1.6, and finally 0.2 + √2 which is approximately 1.614. This confirms the order in option A.
Which of the following lists the numbers in descending order: 0.71, 1/√2, √2/2, and 0.7?
0.71, 0.7, 1/√2, √2/2
0.71, 1/√2, √2/2, 0.7
0.7, √2/2, 1/√2, 0.71
1/√2, √2/2, 0.7, 0.71
Since 1/√2 and √2/2 are equivalent (≈0.7071), the largest number here is 0.71, followed by the equal middle values, and then 0.7. This tests precision in handling both fractions and decimals.
Arrange these expressions in increasing order: 0.333, 1/3, 0.33(3), and 0.34.
0.333, 1/3, 0.34, 0.33(3)
1/3, 0.333, 0.33(3), 0.34
0.33(3), 1/3, 0.333, 0.34
0.333, 1/3, 0.33(3), 0.34
The truncated 0.333 is slightly less than the repeating decimals represented by 1/3 and 0.33(3) (both approximating 0.3333…), while 0.34 is the largest. Option A reflects this nuanced ordering.
Order the following expressions from smallest to largest: 2, (√5 + 2)/2, 2.2, and √5.
(√5 + 2)/2, 2, 2.2, √5
2, 2.2, (√5 + 2)/2, √5
2, 2.2, √5, (√5 + 2)/2
2, (√5 + 2)/2, 2.2, √5
With √5 being approximately 2.236 and (√5 + 2)/2 roughly 2.118, the order from smallest to largest is 2, then (√5 + 2)/2, followed by 2.2, and finally √5.
Determine the correct ascending order for the following numbers: -1.76, -1.75, -√3, and -1.73.
-1.75, -1.76, -1.73, -√3
-1.76, -1.75, -√3, -1.73
-√3, -1.76, -1.75, -1.73
-1.73, -√3, -1.75, -1.76
Approximating √3 as 1.732 means -√3 is about -1.732. Hence, the smallest value is -1.76, followed by -1.75, then -1.732 (i.e. -√3), and finally -1.73 is the largest among these negatives.
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Study Outcomes

  1. Analyze the order of rational and irrational numbers on the number line.
  2. Apply strategies to arrange real numbers in ascending and descending order.
  3. Evaluate numerical expressions to determine their relative magnitude.
  4. Demonstrate understanding of the relationship between fractions, decimals, and irrational numbers.
  5. Explain how absolute value influences the ordering of numbers.

Ordering Real Numbers Worksheet Cheat Sheet

  1. Understand different forms of real numbers - Real numbers come in many shapes: integers, fractions, decimals, and those mysterious irrationals like √2 or π. Recognizing each form makes it easier to convert, compare, and manipulate them confidently. Explore real number forms on Math4Texas
  2. Convert everything to decimals - Turning fractions and mixed numbers into decimals levels the playing field for comparison. When you see ¾ as 0.75 or 5¹/₄ as 5.25, it's a breeze to spot which is larger or smaller. Guide to ordering numbers on GrownUpMath
  3. Approximate irrational numbers - Since √22 or π can't be written exactly, round them to a few decimal places for a fair fight. Approximating √22 to 4.69 and π to 3.14 helps you slot them into your list without sweating the tiny leftover bits. Real numbers worksheet at OnlineMath4All
  4. Visualize with a number line - A number line is your secret weapon for ordering tasks. Plotting each number gives a snapshot of their positions and makes gaps crystal clear. Number line practice at OnlineMath4All
  5. Master negative number rules - Remember: any negative value is always less than any positive one. Among negatives, the one with the larger absolute value sits further left on the number line (so -5 is smaller than -2). Keeping that straight wards off common mix‑ups. Negative number guide on GrownUpMath
  6. Practice mixed radicals and numbers - Mixing square roots with decimals and whole numbers sharpens your ordering skills. Challenge yourself with sets like 2√3, √17, and 3√2, then arrange them from least to greatest. Mixed numbers worksheet at OnlineMath4All
  7. Use absolute value for clarity - Absolute value measures distance from zero, so |-3| equals 3 even though -3 lies on the left side. This trick helps you compare negatives by focusing on how far they are from the origin. Absolute value exercises at Math Salamanders
  8. Convert improper fractions - An improper fraction like 7/2 can disguise its true size. Converting it to the mixed number 3 ½ makes it instantly comparable with other values. Improper-to-mixed conversion on Math Salamanders
  9. Play interactive ordering games - Turn study time into game time with digital tools and quizzes. Timed challenges and rewards keep you motivated while reinforcing your ordering instincts. Ordering games on Math4Texas
  10. Build speed with regular practice - Consistency is key: daily worksheets and problem sets cement concepts and boost your recall. Soon you'll be ordering any mix of fractions, decimals, and roots in a snap. Twinkl practice activity
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