Skip to content 1 Try to extend this method for constructing line segments of lengths sqrt(3) and sqrt(5) using a ruler and a compass.
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2 Consider this puzzle: What is the square root of -1?
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3 The decimal expansion of p/q will be terminating precisely when the prime factors of q are only 2, only 5, or both 2 and 5.
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4 Try to find the decimal expansions of 10/3 and 11/12.
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5 Convert the following rational numbers into the form of a terminating decimal or a non-terminating and repeating decimal, whichever the case may be, by the process of long…
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6 Prove that sqrt(5) is an irrational number.
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7 Convert the following decimal numbers into the form of p/q.
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8 Locate the following rational numbers on the number line.
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9 Find 6 rational numbers between 3 and 4.
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10 Find 5 rational numbers between 2/5 and 3/5.
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11 Find 5 rational numbers between 1/6 and 2/5.
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12 If x/3 + x/5 = 16/15, find the rational number x.
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13 Let a and b be two non-zero rational numbers such that a + 1/b = 0.
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14 A rational number has terminating decimal expansion whose last non-zero digit occurs in the 4th decimal place.
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15 Without performing division, determine whether the decimal expansion of 18/125 is terminating or non-terminating?
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16 A rational number in its lowest form has denominator 23 × 5.
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17 Let a = 7/12 and b = 5/6.
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18 Three rational numbers x, y, z satisfy x + y + z = 0 and xy + yz + zx = 0.
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19 Show that the rational number a+b/2 lies between the rational numbers a and b.
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20 Find the lengths of the hypotenuses of all the right triangles in the given figure which is referred to as the square root spiral.
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21 Find the rational number x such that 5/6 ≤ft(x + 3/5) = 5/6 x + 1/2.
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22 Represent the rational numbers 2/3,-5/4 and 11/2 on a single number line.
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23 Simplify the expression: ≤ft(-1/4)+≤ft(5/12).
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24 Find three distinct rational numbers that lie strictly between -1/2 and 1/4.
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25 Find three rational numbers between 3.1415 and 3.1416. [Page No. 53]
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26 A tailor has 153/4\, meters of fine silk; if making one kurta requires 21/4\, meters of silk, exactly how many kurtas can he make?
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27 Can you think of other way(s) to find a rational number between any two rational numbers?
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28 Without performing long division, determine which of the following rational numbers will have terminating decimals and which will be repeating: 7/20, 4/15 and 13/250.
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29 Perform the long division for 1/13.
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30 Classify the following numbers as rational or irrational:
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