Write $98 \%$ as a reduced fraction.
Answer (1)
Convert the percentage to a fraction: 98% = 100 98 .
Find the greatest common divisor (GCD) of 98 and 100, which is 2.
Divide both the numerator and the denominator by the GCD: 100 ÷ 2 98 ÷ 2 = 50 49 .
The reduced fraction is 50 49 .
Explanation
Converting Percentage to Fraction We need to express 98% as a reduced fraction. First, we convert the percentage to a fraction by dividing by 100. This gives us 100 98 .
Finding the Greatest Common Divisor (GCD) Next, we need to simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 98 and 100 is the largest number that divides both 98 and 100 without leaving a remainder.
Prime Factorization Method We can find the GCD of 98 and 100 using prime factorization or the Euclidean algorithm. Let's use prime factorization:
Prime factorization of 98: 2 × 7 × 7 = 2 × 7 2 Prime factorization of 100: 2 × 2 × 5 × 5 = 2 2 × 5 2
The common factors are 2 . Therefore, the GCD(98, 100) = 2.
Reducing the Fraction Now, we divide both the numerator and the denominator by their GCD, which is 2:
100 ÷ 2 98 ÷ 2 = 50 49
Final Reduced Fraction The fraction 50 49 is in its simplest form because 49 and 50 have no common factors other than 1.
Final Answer Therefore, 98% as a reduced fraction is 50 49 .
Examples
In everyday life, percentages and fractions are often used interchangeably. For instance, if a store advertises a "98% off" sale on an item, it means the item's price is reduced by 100 98 or 50 49 of its original price. Understanding how to convert percentages to fractions helps you quickly determine the actual discount you're receiving. This skill is useful not only for shopping but also for understanding statistics, financial calculations, and many other real-world scenarios where proportions are important.
