Number System
Himachal Pradesh Board · Class 9 · Mathematics
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Which of the following statements is true about zero?
How many rational numbers exist between 1 and 2?
What is 0.333... (0.3̄) equal to?
The decimal expansion of 1/7 is:
Sample Questions
Which of the following are rational numbers?
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3/5, √4, 0.25, -7
Rational numbers can be expressed in the form p/q where p and q are integers and q≠0. 3/5 is already in this form, √4=2 (which is 2/1), 0.25=1/4, and -7=-7/1. √2 is irrational because it cannot be expressed as a fraction.
Every integer is a rational number.
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True
Every integer m can be expressed in the form m/1, where m and 1 are integers and 1≠0. Therefore, every integer is a rational number.
Which of the following are irrational numbers?
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√5, π, 0.101001000100001...
Irrational numbers have non-terminating, non-recurring decimal expansions. √5 and π are well-known irrational numbers. 0.101001000100001... is non-terminating and non-recurring. √9 = 3 (rational) and 22/7 is a fraction (rational).
Every rational number is an integer.
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False
This statement is false. While every integer is a rational number, not every rational number is an integer. For example, 3/5 = 0.6 is a rational number but not an integer.
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