Tag: decimal representation of rational numbers

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Multiple choice decimal representation of rational numbers rational and irrational numbers maths

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

  1. Infinite

  2. Finite but more than one

  3. Exactly one

  4. Zero
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rewriting the given equation by completing the square for x and y terms gives (x - 12)^2 + (y - 13)^2 = 0. Since the sum of squares of real numbers can only be zero if each term is individually zero, there is only one unique real solution pair (12, 13). Therefore, the number of ordered pairs is exactly one.

Multiple choice decimal representation of rational numbers rational and irrational numbers maths

The decimal part of $3.89$ is

  1. $3$
  2. $0.79$
  3. $0.89$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $0.89$.

Multiple choice decimal representation of rational numbers rational and irrational numbers maths

Fractional Part of $2.056$ is?

  1. $0.056$
  2. $0.05$
  3. $0.5$
  4. $0.66$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $0.056$