Rational and Irrational Numbers — Practice Quiz
ICSE · Class 9 · Mathematics
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Quick Quiz: Rational and Irrational Numbers
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Convert the decimal 0.75 to a rational number in its simplest form.
Find three rational numbers between 1/4 and 1/2.
Rationalize the denominator: 1/(3 + √2)
Arrange these numbers in ascending order: √8, 2.5, 22/9, √10
Sample Questions
Which of the following numbers are rational?
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0.333..., √16, 22/7
Step 1: Check each number. 0.333... = 1/3 (recurring decimal = rational). √16 = 4 (perfect square = rational). √7 is non-terminating non-recurring (irrational). 22/7 is already in p/q form (rational). π = 3.14159... is non-terminating non-recurring (irrational).
Calculate: 2√3 × 3√3
The sum of a rational number and an irrational number is always irrational.
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True
Step 1: Let r be rational and i be irrational. Step 2: Assume r + i = q (rational). Step 3: Then i = q - r. Since q and r are both rational, q - r is rational. Step 4: This contradicts that i is irrational. Therefore, r + i must be irrational.
Which of the following are properties of irrational numbers?
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Non-terminating, non-recurring decimals, Cannot be expressed as p/q, Product with non-zero rational is irrational
Step 1: Check each property. Non-terminating, non-recurring decimals ✓. Cannot be expressed as p/q ✓. Sum of two irrationals: (2+√3) + (2-√3) = 4 (rational) ✗. Product with non-zero rational: 2×√3 = 2√3 (irrational) ✓.
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