Sure, let's determine which number is rational among the given options.
A. 0.7
A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero. For this option:
- [tex]\( 0.7 \)[/tex] can be expressed as [tex]\( \frac{7}{10} \)[/tex], which is a fraction of two integers.
- Hence, [tex]\( 0.7 \)[/tex] is a rational number.
B. [tex]\( \sqrt{5} \)[/tex]
A number is irrational if it cannot be expressed as a simple fraction of two integers. For this option:
- [tex]\( \sqrt{5} \)[/tex] is not a perfect square, and its decimal representation is non-terminating and non-repeating.
- Thus, [tex]\( \sqrt{5} \)[/tex] is an irrational number.
C. [tex]\( 0.31243576 \ldots \)[/tex]
This number appears to be a non-terminating and non-repeating decimal sequence. For this option:
- Non-terminating and non-repeating decimals are considered irrational numbers because they cannot be exactly expressed as a fraction of two integers.
- Therefore, [tex]\( 0.31243576 \ldots \)[/tex] is an irrational number.
D. [tex]\( \pi \)[/tex]
The number π (pi) is widely known in mathematics as an irrational number. Its decimal representation goes on forever without repeating. For this option:
- [tex]\( \pi \)[/tex] cannot be exactly expressed as a fraction of two integers.
- Hence, [tex]\( \pi \)[/tex] is an irrational number.
From our analysis:
- A. [tex]\( 0.7 \)[/tex] - Rational
- B. [tex]\( \sqrt{5} \)[/tex] - Irrational
- C. [tex]\( 0.31243576 \ldots \)[/tex] - Irrational
- D. [tex]\( \pi \)[/tex] - Irrational
Therefore, the rational number among these options is:
A. 0.7
