Tag: rational and irrational numbers

Questions Related to rational and irrational numbers

Number of ordered pairs $(x, y)$ of real numbers satisfying the equation $x^{2} + y^{2} - 24x - 26y + 313 = 0$ is equal to

decimal representation of rational numbers rational and irrational numbers maths

  1. Infinite

  2. Finite but more than one

  3. Exactly one

  4. Zero

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Correct Option: D

The number having no reciprocal is

decimal representation of rational numbers rational and irrational numbers maths

  1. $2$

  2. $1$

  3. $-1$

  4. $0$

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Correct Option: D
Explanation:

If a number is 2 then its reciprocal is $\dfrac{1}{2}$

The number '0' has no reciprocal.

The decimal part of $9.99$ is

decimal representation of rational numbers rational and irrational numbers maths

  1. $0.99$

  2. $9$

  3. $8$

  4. $0.98$

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Correct Option: A
Explanation:

Decimal part of $9.99$ is $0.99$.

So, option A is correct.

The integral part of $3.89$ is

decimal representation of rational numbers rational and irrational numbers maths

  1. $3$

  2. $0.89$

  3. $4$

  4. None of these

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Correct Option: A
Explanation:

Integral part of $3.89$ is $3$.

The integral part of $4.20$ is

decimal representation of rational numbers rational and irrational numbers maths

  1. $4$

  2. $2$

  3. $3$

  4. None of these

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Correct Option: A
Explanation:

The integral part of $4.20$ is $4$.

So, option A is correct.

The decimal part of $4.20$ is

decimal representation of rational numbers rational and irrational numbers maths

  1. $4$

  2. $0.20$

  3. $2$

  4. None of these

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Correct Option: B
Explanation:

The decimal part of $4.20$ is $0.20$.

The decimal part of $3.89$ is

decimal representation of rational numbers rational and irrational numbers maths

  1. $3$

  2. $0.79$

  3. $0.89$

  4. None of these

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Correct Option: C
Explanation:

A decimal may have both a whole-number part and a fractional part. 

The whole-number part of a decimal are those digits to the left of the decimal point. 

The fractional part(decimal part) of a decimal is represented by the digits to the right of the decimal point.

Decimal part of $3.89$ is $0.89$.

The integral part of $9.99$ is

decimal representation of rational numbers rational and irrational numbers maths

  1. $9$

  2. $8$

  3. $7$

  4. None of these

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Correct Option: A
Explanation:

Fractional part of $9.99$ is $9$.

So, option A is correct.

The integral part of $63.281$ is?

decimal representation of rational numbers rational and irrational numbers maths

  1. $63$

  2. $0.281$

  3. $26$

  4. $5$

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Correct Option: A
Explanation:

The integer part, or integral part of a decimal number is the part to the left of the decimal separator. The part from the decimal separator to the right is the fractional part.

$\therefore$ Integral part of $63.281$ is $63$

Fractional Part of $2.056$ is?

decimal representation of rational numbers rational and irrational numbers maths

  1. $0.056$

  2. $0.05$

  3. $0.5$

  4. $0.66$

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Correct Option: A
Explanation:

The integer part, or integral part of a decimal number is the part to the left of the decimal separator. The part from the decimal separator to the right is the fractional part.

$\therefore$ Fractional part of $2.056$ is $0.056$