Comparing and Ordering Real Numbers
A Grade 10 math worksheet focusing on comparing and ordering real numbers, including rational and irrational numbers.
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Comparing and Ordering Real Numbers
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Read each question carefully and follow the instructions. Show all your work where applicable.
1. A number that can be expressed as a fraction p/q where p and q are integers and q ≠ 0 is called a number.
2. Numbers that cannot be expressed as a simple fraction are called numbers.
3. The set of all rational and irrational numbers is called the set of numbers.
4. Which of the following is an irrational number?
0.333...
√9
π
-5
5. Which inequality is true?
√2 < 1.4
π > 3.1416
1/3 > 0.33
-7 < -8
6. Use <, >, or = to compare the following numbers:
a) √16 4
b) 0.75 3/4
c) -1/2 -0.6
d) 2.5 √5
7. Order the following numbers from least to greatest. Show your work or explain your reasoning.
2.7, √7, 2 3/4, 2.755
-3.1, -π, -3.14, -√10
8. Plot the following numbers on the number line below: -2.5, 0, √3, 7/2
9. A rectangular garden has a length of √121 meters and a width of 10.5 meters. Is the length or the width greater? Explain your answer.
10. All integers are rational numbers.
True
False
11. The product of two irrational numbers is always irrational.
True
False