Find three different irrational numbers between the rational numbers 5/7 and 9/11 .

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Chapter 1

NCERT

Class 9

Mathematics

Solutions

8. Find three different irrational numbers between the rational numbers 5/7 and 9/11 .

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Question:

Find three different irrational numbers between the rational numbers 5/7 and 9/11 .

Answer:

Decimal representation of rational number 5/7

Now, decimal representation of rational number 9/11

The required irrational numbers will lie between 0.714285 and 0.81. Also, the irrational numbers have non-terminating non-recurring.

∴ Required three irrational numbers are:

0.75075007500075000075..., 0.7676076007600076...... and 0.80800800080000...

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(All Q's of this Chapter solved)

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Simplify : (i) 2^1/3.2 ^1/5

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Find : (i) 9^3/2

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Find : (i) 64 1/2

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Rationalise the denominators each of the following :

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Represent √9.3 on the number line.

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Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = c/d . This seems to contradict the fact that π is irrational. How will you resolve this contradiction ?

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Simplify each of the following expressions :

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Classify the following numbers as rational or irrational: (i) 2 − √5

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Classify the following numbers as rational or irrational :

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Write three numbers whose decimal expansions are non-terminating non-recurring.

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Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions).

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What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17 ? Perform the division to check your answer.

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Express 0.999999.... in the form p/q . Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense ?

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Express the following in the form p/q , where p and q are integers and q ≠ 0 :

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You know that 1/7 = 0.142857 . Can you predict what the decimal expansions of 2/7 , 3/7 , 4/7 , 5/7 , 6/7 are, without actually doing the long division ? If yes, how ?

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Write the following in decimal form and say what kind of decimal expansion each has :

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Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion.

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Show how √5 can be represented on the number line.

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Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

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State whether the following statements are true or false. Justify your answer.

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State whether the following statements are true or false. Give reasons for your answers.

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3. Find five rational numbers between 3/5 and 4/5.

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Find six rational numbers between 3 and 4.

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Is zero a rational number ? Can you write it in the form p q , where p and q are integers and q ≠ 0 ?

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