The World of Numbers — Important Questions
CBSE · Class 9 · Mathematics
89 important questions from The World of Numbers for CBSE Class 9 Mathematics, with answers. Part of the CBSE Class 9 Mathematics syllabus.
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Important Questions from The World of Numbers
A decimal 2.35 overline 7 is converted into a fraction. What is its value as p/q?
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1061/450
Let x = 2.35 overline 7. Multiply by 100 to move the non-repeating digits: 100x = 235.overline 7. Multiply again by 10: 1000x = 2357.overline 7. Subtract: 1000x - 100x = 2357.overline 7 - 235.overline 7 = 2122. So 900x = 2122 and x = 2122/900 = 1061/450.
A fraction 2/3 is compared with 4/6. Which statement about these rational numbers is correct?
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They are equal, They satisfy ad = bc
Check equality using cross multiplication: 2 × 6 = 12 and 3 × 4 = 12. Since ad = bc, the fractions are equal. Different denominators do not mean different values.
Which properties are true for rational numbers?
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They are closed under addition, They are closed under subtraction, They are closed under multiplication
Rational numbers remain rational after addition, subtraction, and multiplication. They are also closed under division as long as division by zero is avoided. So the statement that they are never closed under division is false.
A fraction 3/20 is written as a decimal. Which statements are correct?
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It equals 0.15, It is a terminating decimal, Its denominator has only 2 and 5 as prime factors after simplification
3/20 = 3/(2^2 × 5). Multiplying numerator and denominator by 5 gives 15/100 = 0.15. Since the denominator can become a power of 10, the decimal terminates.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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