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The product of a rational number and irrational number is always irrational.

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Important Questions on Number Systems

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If x=0.7¯ then what is the value of 2x?
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The terminating decimal expansion of the number 337125 is _____
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Which one of the following is a non - terminating repeating decimal?

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Which one of the following decimal numbers is a rational number with denominator 37?

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Find such number, so that one fourth of the number is 8 more than 5:

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Write the terminating decimal numeral for 1732.

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Write 211 in decimal form and say what kind of decimal expansion it has?

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Write the terminating decimal numeral for 74.

HARD

D is a real number with non terminating digits a1 and a2 after the decimal point. Let D=0.a1a2a1a2.. with a1and a2 both of zero which of the following when multiplied by D will necessarily give an integer ?

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Write 36100 in decimal form and say what kind of decimal expansion it has?
 
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Write 313 in decimal form and say what kind of decimal expansion it has?
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If 0.001 is expressed in the simplest form as pq, where p and q are integers and q0, then find the value of p+q.
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The decimal representation of a rational number cannot be:
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Write the terminating decimal numeral for 2950.

MEDIUM
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 117? Perform the division to check your answer.
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Write 418 in decimal form and say what kind of decimal expansion each has?
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Express the mixed recurring decimal 4.32¯ in the form of pq
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Write 329400 in decimal form and say what kind of decimal expansion it has?
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Identify whether the number 7.478478.... is Rational Number / Irrational Number.