What fration is equvint to 0.65

General
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what fration is equvint to 0.65

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What fraction is equivalent to 0.65?

Answer:

When you want to convert a decimal to a fraction, you essentially want to express that decimal as a ratio of two integers. Let’s break down the process of converting 0.65 into a fraction step by step.

Step 1: Understand the Decimal Notation

The decimal 0.65 can be read as “sixty-five hundredths,” which provides a direct clue on how to express it as a fraction. Decimals represent parts of a whole, and in the case of 0.65, each digit has a specific place value:

  • The digit ‘6’ is in the tenths place.
  • The digit ‘5’ is in the hundredths place.

This means 0.65 is made up of 65 parts out of 100.

Step 2: Write as a Fraction

Given that 0.65 reads as “sixty-five hundredths,” you can write it directly as a fraction:

\frac{65}{100}

This fraction simply means that 65 parts out of 100 make up the number 0.65.

Step 3: Simplify the Fraction

Fractions are typically expressed in their simplest form, which means reducing the numerator and denominator to their smallest possible integers while maintaining the equivalence to the original fraction. Here is how to simplify the fraction \frac{65}{100}:

  1. Find the Greatest Common Divisor (GCD): The GCD of two numbers is the largest integer that divides both numbers without leaving a remainder. For 65 and 100, let’s determine the GCD.

    • Factors of 65: 1, 5, 13, 65
    • Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

    The common factors are 1 and 5, with 5 being the greatest.

  2. Divide the Numerator and Denominator by their GCD: Using the GCD, which is 5, divide both the numerator and the denominator of the fraction \frac{65}{100}.

    • Divide 65 by 5: 65 \div 5 = 13
    • Divide 100 by 5: 100 \div 5 = 20

    Thus, the simplified form of \frac{65}{100} is:

    \frac{13}{20}

Final Answer:

The fraction equivalent to 0.65 is \frac{13}{20}. This is the fraction written in its simplest form. Understanding this conversion helps in various mathematical tasks, such as arithmetic operations with decimals and fractions, and applying these concepts in real-life problems.

By transforming the decimal into a fraction, you enhance your grasp of how numbers can be expressed in different formats, which is a valuable skill in both academic and practical scenarios. The fraction \frac{13}{20} captures the exact value of 0.65 just as precisely as any other representation, serving as a reminder of the versatility and elegance of numbers.