Write 130% as a fraction in lowest terms.
The Correct Answer and Explanation is :
To express 130% as a fraction in its lowest terms, let’s follow these steps:
Step 1: Convert Percentage to a Fraction
A percentage is simply a fraction with a denominator of 100. So, to convert 130% to a fraction, we can write it as:
[
130\% = \frac{130}{100}
]
Step 2: Simplify the Fraction
Now, we need to simplify the fraction (\frac{130}{100}). This means finding the greatest common divisor (GCD) of 130 and 100.
We begin by finding the prime factorizations of 130 and 100:
- The prime factorization of 130 is (130 = 2 \times 5 \times 13).
- The prime factorization of 100 is (100 = 2 \times 2 \times 5 \times 5).
The common factors between 130 and 100 are 2 and 5. The greatest common divisor (GCD) is the product of these common factors, so:
[
GCD(130, 100) = 2 \times 5 = 10
]
Step 3: Divide the Numerator and Denominator by the GCD
Now, simplify (\frac{130}{100}) by dividing both the numerator and denominator by the GCD, which is 10:
[
\frac{130 \div 10}{100 \div 10} = \frac{13}{10}
]
Final Answer:
Thus, 130% as a fraction in its lowest terms is:
[
\frac{13}{10}
]
Explanation:
The percentage represents a part of 100, so to convert a percentage to a fraction, you place the percentage value as the numerator and 100 as the denominator. Afterward, simplifying the fraction ensures that we express it in its simplest form. In this case, by dividing both the numerator and denominator by their greatest common divisor (10), we arrive at the simplified fraction (\frac{13}{10}). This fraction means that 130% is equivalent to 1 and (\frac{3}{10}), or one and three-tenths when expressed as a mixed number.