Identify which condition is necessary for a number to be rational.(1 point)

Question

Responses

It must not be negative.
It must not be negative.

It must be written as a fraction.
It must be written as a fraction.

It must be able to be expressed as an integer divided by a nonzero integer.
It must be able to be expressed as an integer divided by a nonzero integer.

It must not be an endless decimal.

Which of the following is irrational?(1 point)
Responses

3√4
Start Fraction Start Root 3 End Root over 4 End Fraction

52.781654292
52.781654292

−7837
negative 7 Start Fraction 8 over 37 End Fraction

3.6363636363636363...
3.6363636363636363...

Answer 1

To answer your questions:

1. The condition necessary for a number to be rational is: It must be able to be expressed as an integer divided by a nonzero integer.

2. Among the options you provided, the irrational number is: 52.781654292 (Since it is a decimal that does not have a repeating segment or terminate, making it potentially non-rational).

All other options would be considered rational.

• \(3\sqrt{4}\) simplifies to \(6\), which is rational.
• \(-7837\) can be expressed as \(-7837/1\), making it rational.
• \(3.6363636363636363...\) is a repeating decimal and can be represented as a fraction, hence it is rational as well.

Therefore, the correct answers are:

1. It must be able to be expressed as an integer divided by a nonzero integer.
2. 52.781654292 (the irrational number).