Which decimal is equivalent of 6/11
The Correct Answer and Explanation is :
To find the decimal equivalent of the fraction ( \frac{6}{11} ), we can perform the division of the numerator (6) by the denominator (11).
Calculation
- Long Division Method:
- Divide 6 by 11. Since 6 is less than 11, we write 0 and add a decimal point, making it 6.0.
- Now, consider 60. 11 goes into 60 five times (since ( 11 \times 5 = 55 )).
- Subtract 55 from 60, which gives us a remainder of 5.
- Bring down another 0 to make it 50.
- 11 goes into 50 four times (since ( 11 \times 4 = 44 )).
- Subtract 44 from 50 to get a remainder of 6.
- Repeat the process by bringing down another 0, which again gives us 60.
This cycle continues, repeating the steps: 5, 4, then 5, 4, and so on.
Thus, the decimal representation of ( \frac{6}{11} ) is ( 0.545454…), which can be noted as ( 0.\overline{54} ) to indicate that the digits 54 repeat indefinitely.
Explanation
The fraction ( \frac{6}{11} ) consists of two components: a numerator (6) and a denominator (11). The denominator represents the total number of equal parts, while the numerator indicates how many of those parts we have.
When we convert fractions to decimals, we often seek to express them in a form that is easier to understand and work with, particularly in mathematical calculations. The long division method allows us to visualize how fractions can be expressed as decimal numbers.
In everyday use, decimals provide a convenient way to represent portions of a whole, which can be critical in fields like finance, science, and engineering, where precise measurements are necessary. Knowing how to convert fractions to decimals helps improve our numerical fluency and allows us to better manipulate numbers in various contexts.
In summary, ( \frac{6}{11} ) is equivalent to the decimal ( 0.\overline{54} ), showcasing a repeating pattern that highlights the infinite nature of certain fractions when expressed as decimals.