What is 0.6 as a fraction is simplest form
The Correct Answer and Explanation is :
The correct answer is: ( \frac{3}{5} )
To convert the decimal (0.6) into a fraction in its simplest form, we can follow these steps:
- Write the decimal as a fraction: The decimal (0.6) can be expressed as ( \frac{6}{10} ). This is because (0.6) is equivalent to six tenths.
- Simplify the fraction: To simplify the fraction ( \frac{6}{10} ), we need to find the greatest common divisor (GCD) of the numerator (6) and the denominator (10). The GCD is the largest number that divides both numbers without leaving a remainder.
- The factors of (6) are (1, 2, 3, 6).
- The factors of (10) are (1, 2, 5, 10). The common factors are (1) and (2), and the greatest common factor is (2).
- Divide both the numerator and the denominator by the GCD: We divide both the numerator and denominator by (2): [
\frac{6 \div 2}{10 \div 2} = \frac{3}{5}
]
Thus, (0.6) as a fraction in its simplest form is ( \frac{3}{5} ).
Explanation of the Process
Converting a decimal to a fraction involves understanding the place value of the decimal. The digit (6) in (0.6) is in the tenths place, hence the denominator is (10). Once you have the initial fraction, the next step is simplification. Simplifying fractions involves reducing them to their lowest terms, making them easier to understand and use.
Finding the GCD is a crucial part of this process because it ensures that you are expressing the fraction in the simplest form. Simplifying helps avoid confusion, especially when performing further calculations or comparisons with other fractions.
Ultimately, recognizing the decimal and applying these basic fraction operations allows for clear and concise mathematical communication. The final fraction, ( \frac{3}{5} ), effectively represents the decimal (0.6) in a form that can be easily used in calculations, comparisons, and real-world applications.