Tag: real number

Questions Related to real number

If $x =\dfrac{p}{q}$  be a rational number such that the prime factorization of $q$ is not of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which is terminating.

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. True

  2. False

  3. Neither

  4. Either

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Correct Option: B
Explanation:

If q is not of the form $2^n*5^m$ then definitely q can take any of the values 3,6,9,12,15,...etc.
As we know 4/3,20/6 all are non-terminating, thus required decimal expansion is non terminating.

The numbers 7.478478.... and 1.101001000100001.....are

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. Rational and irrational respectively

  2. Both rationals

  3. Both irrationals

  4. None of these

Show answer
Correct Option: A
Explanation:

In 7.478478.......  we can see that after decimal the digits 478 are repeating itself again and again.

Hence it is a non-terminating and repeating decimal. Therefore it is a rational number.

In 1.101001000100001........  it is a non-terminating and non-repeating decimal.
Therefore it is an irrational number.
Hence option A is correct.