How do u show the group of digits that repeat in a repeating decimal
To show the group of digits that repeat in a repeating decimal, you can use a horizontal line, called a vinculum, over the repeating group of digits. The vinculum indicates that the numbers underneath it repeat indefinitely. For example, if the decimal 0.333... repeats, you can write it as 0.3̅. Similarly, if the decimal 0.142857142857... repeats, you can write it as 0.142857̅.
To identify the group of digits that repeat in a repeating decimal, you can follow these steps:
1. Recognize the pattern: Look for a set of digits that repeat continuously in the decimal representation. The repetition may start after a certain number of non-repeating digits.
2. Represent the repeating part as a fraction: Let's assume the repeating digits are represented by "x". Count the number of repeating digits, usually referred to as "n". Then, consider the repeating part as the numerator and a number with the same number of 9s in the denominator. For example, if the repeating part is "456," and there are three repeating digits, you would represent it as 456/999.
3. Simplify the fraction: Reduce the fraction to its simplest form, if possible. Use the mathematical operations to divide both the numerator and denominator by their greatest common divisor. In the example above, 456/999 can be simplified to 152/333 since the greatest common divisor of 456 and 999 is 3.
Hence, to show the group of digits that repeat in a repeating decimal, you need to recognize the pattern, represent it as a fraction, and simplify the fraction if necessary.