To classify the number [tex]\(\frac{3}{8}\)[/tex], let's examine it in detail.
1. Convert the fraction into a decimal:
To convert the fraction [tex]\(\frac{3}{8}\)[/tex] into a decimal, perform the division [tex]\(3 \div 8\)[/tex]. This yields [tex]\(0.375\)[/tex].
2. Determine if the decimal representation is terminating or repeating:
The decimal [tex]\(0.375\)[/tex] is a terminating decimal because it ends after the digit 5.
3. Classify the number as rational or irrational:
- A rational number is any number that can be represented as a fraction where both the numerator and the denominator are integers and the denominator is not zero.
- An irrational number cannot be expressed as a simple fraction and has a non-terminating, non-repeating decimal expansion.
Since [tex]\(\frac{3}{8}\)[/tex] can be expressed as the fraction of two integers (3 and 8), and its decimal representation [tex]\(0.375\)[/tex] is terminating, it is a rational number.
4. Choose the correct classification:
The given options are:
- irrational number, [tex]\(0 \overline{375}\)[/tex]
- irrational number, 0.375
- rational number, [tex]\(0 \overline{375}\)[/tex]
- rational number, 0.375
Since [tex]\(\frac{3}{8}\)[/tex] equals [tex]\(0.375\)[/tex] which is a rational number, the correct classification is:
rational number, 0.375
