Question
Which is the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction?
irrational number, 0.6ModifyingAbove 25 with bar
irrational number, 0.625
rational number, 0.625
rational number, 0.6ModifyingAbove 25 with bar
irrational number, 0.6ModifyingAbove 25 with bar
irrational number, 0.625
rational number, 0.625
rational number, 0.6ModifyingAbove 25 with bar
Answers
GPT-4o mini
The fraction \(\frac{5}{8}\) is a rational number because it can be expressed as the ratio of two integers (5 and 8).
To find its decimal expansion, you can perform the division \(5 \div 8\), which gives us 0.625.
Now, let's look at the classifications:
- **Irrational numbers** cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions. Since \(\frac{5}{8}\) is rational, it is not irrational.
- **Rational numbers** can be expressed as fractions of integers and have either terminating or repeating decimal expansions. Since \(0.625\) is a terminating decimal, it is indeed a rational number.
Therefore, the correct classification and decimal expansion of \(\frac{5}{8}\) is:
**rational number, 0.625**.
To find its decimal expansion, you can perform the division \(5 \div 8\), which gives us 0.625.
Now, let's look at the classifications:
- **Irrational numbers** cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions. Since \(\frac{5}{8}\) is rational, it is not irrational.
- **Rational numbers** can be expressed as fractions of integers and have either terminating or repeating decimal expansions. Since \(0.625\) is a terminating decimal, it is indeed a rational number.
Therefore, the correct classification and decimal expansion of \(\frac{5}{8}\) is:
**rational number, 0.625**.