Write the decimal number 0.65 as a fraction reduced to lowest terms

General
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write the decimal number 0.65 as a fraction reduced to lowest terms.

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LectureNotes said write the decimal number 0.65 as a fraction reduced to lowest terms.

Answer:

To write the decimal number 0.65 as a fraction reduced to lowest terms, follow these steps:

1. Convert the Decimal to a Fraction

First, express 0.65 as a fraction:

0.65 = \frac{65}{100}

2. Simplify the Fraction

To reduce the fraction to its lowest terms, find the Greatest Common Divisor (GCD) of the numerator and the denominator.

The numerator is 65 and the denominator is 100. We need to find the GCD of these two numbers.

Prime Factorization:

  • 65: The prime factors of 65 are 5 and 13 because ( 65 = 5 \times 13 ).
  • 100: The prime factors of 100 are 2, 2, 5, and 5 because ( 100 = 2^2 \times 5^2 ).

Common Factors:

Identify the common prime factors. Both 65 and 100 share the prime factor 5.

Greatest Common Divisor (GCD):

Since 5 is the only common prime factor, the GCD is 5.

3. Divide the Numerator and Denominator by Their GCD

Now, divide both the numerator and the denominator by their GCD:

\frac{65}{100} = \frac{65 \div 5}{100 \div 5} = \frac{13}{20}

Therefore, the fraction 0.65 reduced to its lowest terms is:

\boxed{\frac{13}{20}}

This means that the decimal 0.65 is the equivalent of the fraction \frac{13}{20} when expressed in simplest form.