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RD Chapter 1 Real Numbers Ex 1.6 Solutions

Question - 1 : - Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Answer - 1 : -


Since, the denominator is of the form 2m x5n, the rational number has aterminating decimal expansion.

Question - 2 : - Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m x 5n, where m and n are non-negative integers:

Answer - 2 : -


Question - 3 : - Write the denominator of the rational number 257/5000 in the form 2m x 5n , where m, n are non-negative integers. Hence, write the decimal expansion, without actual division.

Answer - 3 : -


Question - 4 : - What can you say about the prime factorisations of the denominators of the following rationals :

Answer - 4 : -

(i) 43.123456789
This decimal fraction is terminating Its denominator will be factorised in theform of 2m x 5n where m and n are non-negativeintegers.

This decimal fraction is non-terminating repeating decimals.
The denominator of their fraction will be not in the form of 2m x 5n wherem and n are non-negative integers.

This decimal fraction is terminating
Its denominator will be factorised in the form of 2m x5n where m and n are non-negativeintegers
(iv) 0.120120012000120000 ………..
This decimal fraction in non-terminating non recurring
Its denominator will not be factorised in the form of 2m x5n where m and n are non negativeintegers

Question - 5 : - A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form p/q ? Give reasons. [NCERT Exemplar]

Answer - 5 : -

327.7081 is terminating decimal number. So, it represents a rational number and also its denominator must have the form 2m x 5n.
 
Hence, the prime factors of q is 2 and 5.

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