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Standard IX

Mathematics

Decimal Expansion of Rational and Irrational Numbers

Which of the ...

Question

Which of the following numbers can be represented as non-terminating, repeating decimals?

$\frac{39}{24}$

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$\frac{3}{16}$

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$\frac{3}{11}$

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$\frac{137}{25}$

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Solution

The correct option is C
$\frac{3}{11}$

$\frac{3}{11}$ as its denominator has no factor of 2 or 5 or both, so it has non-terminating, repeating decimal representation.

Rest of the fractions $(\frac{39}{24} = \frac{13}{8}, \frac{3}{16}, \frac{137}{25})$ have 2 or 5 as a factor of the denominator.

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Similar questions

Q. Which of the following numbers can be represented as non-terminating, repeating decimals?

(a)

\frac{39}{24}

(b)

\frac{3}{16}

(c)

\frac{3}{11}

(d)

\frac{137}{25}

Q. State 'T' for true and 'F' for false.
(i) Every rational number can be expressed with a positive numerator.
(ii)

\frac{3}{11}

cannot be represented as a non-terminating repeating decimal.
(iii) If

\frac{p}{q}

and

\frac{r}{s}

are two terminating decimals, then

\frac{p}{q} \times \frac{r}{s}

is also a terminating decimal.
(iv) If

\frac{p}{q}

is non-terminating repeating decimal and

\frac{r}{s}

is a terminating decimal, then (

\frac{p}{q} \div \frac{r}{s}

) is a terminating decimal.

Which of the following rational number can be represented as terminating and which as non terminating decimals? give the answer without actual dividing

1- 13/8

2- -7/15

The numbers which have a non-terminating and non-repeating decimal expansion and cannot be represented in the form of $\frac{p}{q}$ ( q is not equal to '0') are known as ___ numbers.

Q. Which of the following is a non-terminating, non-repeating decimal number?

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Which of the following numbers can be represented as non-terminating, repeating decimals?

The correct option is C 311 311 as its denominator has no factor of 2 or 5 or both, so it has non-terminating, repeating decimal representation. Rest of the fractions (3924=138,316,13725) have 2 or 5 as a factor of the denominator.

The correct option is C
$\frac{3}{11}$

$\frac{3}{11}$ as its denominator has no factor of 2 or 5 or both, so it has non-terminating, repeating decimal representation.

Rest of the fractions $(\frac{39}{24} = \frac{13}{8}, \frac{3}{16}, \frac{137}{25})$ have 2 or 5 as a factor of the denominator.