Is 5 1/25 rational or irrational?
Understand the Problem
The question is asking whether the number 5 1/25, which is a mixed number, is classified as a rational or irrational number. To address this, we need to convert it into an improper fraction or decimal and analyze its properties.
Answer
The number \( 5 \frac{1}{25} \) is a rational number.
Answer for screen readers
The number ( 5 \frac{1}{25} ) is a rational number.
Steps to Solve
- Convert the mixed number to an improper fraction
To convert the mixed number ( 5 \frac{1}{25} ) to an improper fraction, use the formula:
$$ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} $$
For our case:
$$ 5 \frac{1}{25} = \left(5 \times 25 + 1\right) / 25 = \left(125 + 1\right) / 25 = \frac{126}{25} $$
- Determine if the fraction is rational or irrational
A number is considered rational if it can be expressed as a fraction of two integers (where the denominator is not zero). The fraction ( \frac{126}{25} ) consists of two integers (126 and 25), and since the denominator (25) is not zero, it is a rational number.
The number ( 5 \frac{1}{25} ) is a rational number.
More Information
Rational numbers can always be expressed as fractions or terminating/repeating decimals. In this case, ( \frac{126}{25} ) can be divided to obtain a decimal form, approximately ( 5.04 ), which confirms it is a rational number.
Tips
- Confusing mixed numbers with decimals. Always remember that mixed numbers can be converted into improper fractions to determine their classification.
- Assuming that all numbers with decimals are irrational; many decimals can be rational.