Class 9 Real Numbers on the Number Line — practice questions with answers
Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. On the number line, how many real numbers lie between the integers 2 and 3?
ANone
BExactly one
CExactly ten
DInfinitely many
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Answer: D) Infinitely many
Between any two distinct real numbers there are infinitely many real numbers. So between 2 and 3 there are infinitely many.
2. On the number line, the point P is at 4 and the point Q is at -2. What is the coordinate of the midpoint of segment PQ?
A0
B1
C3
D2
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Answer: B) 1
Midpoint = (4 + (-2))/2 = 2/2 = 1.
3. Between 0 and 1 on the number line, which of these decimals lies furthest to the right (largest)?
A0.45
B0.5
C0.405
D0.54
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Answer: D) 0.54
Comparing: 0.405 < 0.45 < 0.5 < 0.54. The largest is 0.54, so it is furthest right.
4. On the number line, mark the points -0.5, 41, −43 and 0.6. Counting from the left, which position (1st, 2nd, 3rd or 4th) does 41 take?
A1st
B2nd
C3rd
D4th
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Answer: C) 3rd
As decimals: −43 = -0.75, -0.5, 41 = 0.25, 0.6. In order: -0.75, -0.5, 0.25, 0.6. So 41 (0.25) is the 3rd from the left.
5. A surveyor marks pegs on a straight road treated as a number line (in km). Peg A is at -1.5, peg B is at 4.5. He must place peg C so that the distance AC is to CB as 1 is to 2 (AC:CB = 1:2). At what km mark should peg C be placed?
A0.5
B1
C0
D0.25
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Answer: A) 0.5
Total AB = 4.5 - (-1.5) = 6 km. AC:CB = 1:2 means AC = 31(6) = 2 km. C = -1.5 + 2 = 0.5 km.