Repeating decimals are less than the denominator because they represent a fraction that is less than 1. The repeating decimal pattern indicates that the numbers after the decimal point continue infinitely, making it smaller than the whole number represented by the denominator.
To convert a repeating decimal to a fraction, write the repeating decimal as x followed by a bar over the repeating digits. Then, subtract x from x with the bar over it. Finally, divide the resulting number by a number of 9s equal to the number of repeating digits in the original decimal. This will give you the fraction equivalent of the repeating decimal.
No, a repeating decimal cannot be equal to its denominator. A repeating decimal is always less than its denominator because it represents a fraction that is less than 1.
A terminating decimal is a decimal number that ends after a certain number of digits, while a repeating decimal has a repeating pattern of digits after the decimal point. Terminating decimals can be easily converted to fractions, while repeating decimals require a specific method to convert to fractions.
Repeating decimals are important in mathematics because they allow us to accurately represent certain fractions that cannot be written as terminating decimals. They also demonstrate the concept of infinity and the idea that some numbers cannot be fully expressed in decimal form.