How do you show the group of digits that repeat in a repeating decimal
13/3 = 4.3333333..........
if writing by hand, you place a bar over the repeated digits.
If typing online, underlining might work for you, as in
12.3463265
To show the group of digits that repeat in a repeating decimal, you can follow these steps:
Step 1: Identify the repeating decimal. This is a decimal representation of a fraction where one or more digits repeat endlessly.
Step 2: Determine the length of the repeating pattern. This can be done by noting the number of digits that repeat before a different digit appears.
Step 3: Use a notation method to represent the repeating pattern. In mathematics, a bar is commonly placed over the repeating pattern to indicate its repetition. For example, if the decimal pattern is 0.123123123..., the repeating pattern can be denoted as 0.123 with a bar over it.
By following these steps, you can clearly show the group of digits that repeat in a repeating decimal.
To show the group of digits that repeat in a repeating decimal, you need to perform a mathematical process called long division. Here's how you can do it step by step:
Step 1: Write down the repeating decimal number, for example, 0.666...
Step 2: Multiply the decimal number by a power of 10 that shifts the repeating part to the left of the decimal point, so that it becomes a whole number. In the example, multiply 0.666... by 10, which gives you 6.666...
Step 3: Set up a long division problem with the multiplied number as the dividend and the original decimal number as the divisor. In our example, the dividend is 6.666... and the divisor is 0.666...
Step 4: Perform long division by dividing the dividend by the divisor. Write down the quotient, but instead of writing down the remainder as usual, bring it down as part of the dividend.
Step 5: Keep repeating step 4 until the pattern of the remainders repeats itself. The repeated digits will form the group of digits that repeat in the decimal.
For example, when dividing 6.666... by 0.666..., you will get a quotient of 10 and a remainder of 0. This means that the group of digits "6" in the original decimal are the repeating digits.
So, in general, to find the group of digits that repeat in a repeating decimal, perform long division until the remainders start repeating, and the repeating remainders will form the group of repeating digits in the decimal.