is 2 and1/42 a rational number

Question

GPT-4o mini · Answer

Yes, $ 2 \frac{1}{42} $ is a rational number. A rational number is defined as a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. To express $ 2 \frac{1}{42} $ as an improper fraction, you can convert it as follows: $$ 2 \frac{1}{42} = 2 + \frac{1}{42} = \frac{2 \times 42}{42} + \frac{1}{42} = \frac{84}{42} + \frac{1}{42} = \frac{85}{42} $$ Since $ \frac{85}{42} $ is a fraction where both the numerator (85) and denominator (42) are integers, it confirms that $ 2 \frac{1}{42} $ is indeed a rational number.

yayy · Answer

is 1 and 5/24 a rational number

GPT-4o mini · Answer

Yes, $ 1 \frac{5}{24} $ is a rational number. Rational numbers are defined as numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. To convert $ 1 \frac{5}{24} $ into an improper fraction, you can do the following: $$ 1 \frac{5}{24} = 1 + \frac{5}{24} = \frac{1 \times 24}{24} + \frac{5}{24} = \frac{24}{24} + \frac{5}{24} = \frac{29}{24} $$ Since $ \frac{29}{24} $ is an improper fraction where both the numerator (29) and denominator (24) are integers, it confirms that $ 1 \frac{5}{24} $ is indeed a rational number.

yayy · Answer

which of the following is rational number the square root of 30 pi 0 the square root of 84

GPT-4o mini · Answer

To determine which of the given numbers are rational, let's evaluate each one:

The square root of 30 ($\sqrt{30}$): This is an irrational number because 30 is not a perfect square.
Pi ($\pi$): This is also an irrational number. It cannot be expressed as a fraction of two integers.
0: This is a rational number because it can be expressed as $\frac{0}{1}$ or $\frac{0}{n}$ (where $n$ is any non-zero integer).
The square root of 84 ($\sqrt{84}$): This is an irrational number as 84 is not a perfect square. It can be expressed as $\sqrt{4 \times 21} = 2\sqrt{21}$, where $\sqrt{21}$ is irrational.

Conclusion:

The only rational number from the list is 0.

yayy · Answer

which of the following is a rational number the square root of 73 the square root of 34 -2 and 1/6 pi

GPT-4o mini · Answer

To determine which of the given numbers are rational, let's evaluate each one:

The square root of 73 ($\sqrt{73}$): This is an irrational number because 73 is not a perfect square.
The square root of 34 ($\sqrt{34}$): This is also an irrational number because 34 is not a perfect square.
$-2 \frac{1}{6}$: This is a rational number. It can be converted to an improper fraction: \[ -2 \frac{1}{6} = -2 - \frac{1}{6} = -\frac{12}{6} - \frac{1}{6} = -\frac{13}{6} \] Since $-\frac{13}{6}$ is a fraction where both the numerator (-13) and the denominator (6) are integers, it is a rational number.
Pi ($\pi$): This is an irrational number. It cannot be expressed as a fraction of two integers.

Conclusion:

The only rational number from the list is $-2 \frac{1}{6}$.

yayy · Answer

which of the following is a rational number the square root of 45 the square root of 17 -99

GPT-4o mini · Answer

To determine which of the given numbers are rational, let's evaluate each one:

The square root of 45 ($\sqrt{45}$): This is an irrational number because 45 can be expressed as $9 \times 5$, and $\sqrt{45} = 3\sqrt{5}$ where $\sqrt{5}$ is irrational.
The square root of 17 ($\sqrt{17}$): This is also an irrational number because 17 is not a perfect square.
-99: This is a rational number because it can be expressed as $-\frac{99}{1}$, which is a fraction of two integers.

Conclusion:

The only rational number from the list is -99.

yayy · Answer

which of the following is a rational number the square root of 44 1 and 4/42 the square root of 80

GPT-4o mini · Answer

To determine which of the given numbers are rational, let's evaluate each one:

The square root of 44 ($\sqrt{44}$): This number is irrational because 44 can be expressed as $4 \times 11$, and $\sqrt{44} = 2\sqrt{11}$ where $\sqrt{11}$ is irrational.
$1 \frac{4}{42}$: This number is a rational number. We can convert it to an improper fraction: \[ 1 \frac{4}{42} = 1 + \frac{4}{42} = \frac{1 \times 42}{42} + \frac{4}{42} = \frac{42}{42} + \frac{4}{42} = \frac{46}{42} \] The fraction $\frac{46}{42}$ can be simplified, but it is already a valid representation of a rational number.
The square root of 80 ($\sqrt{80}$): This number is also irrational because 80 can be expressed as $16 \times 5$, and $\sqrt{80} = 4\sqrt{5}$ where $\sqrt{5}$ is irrational.

Conclusion:

The only rational number from the list is $1 \frac{4}{42}$ (or $\frac{46}{42}$).