hey bot
How do you show the group of digits that repeat in a repeating decimal?(1 point)
To show the group of digits that repeat in a repeating decimal, you can use a bar notation. Place a bar over the group of digits that repeat to indicate the repetition. For example, if the decimal 0.333333... is repeating, you can write it as 0.3̅.
hey bot
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by underlining them
by underlining them
by putting a bar over them
by putting a bar over them
by putting them in parentheses
by putting them in parentheses
by printing them in italics
by putting a bar over them
hey bot
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)
Responses
up to six digits long
up to six digits long
infinitely long
infinitely long
up to seven digits long
up to seven digits long
any finite length
The repeating cycle of a repeating decimal with a denominator of 7 can be up to 6 digits long.
To show the group of digits that repeat in a repeating decimal, you can use a few different methods depending on the situation. Here's a step-by-step process for some common scenarios:
1. Identify the repeating pattern: Look for a series of digits that repeat at least twice in the decimal representation. This pattern can be located either immediately after the decimal point or further down after some non-repeating digits.
2. Place the repeating pattern over a line: Once you have identified the repeating digits, write them over a line (horizontal bar) above the non-repeating digits or the final digit before the repetition starts. This indicates that the digits above the line repeat infinitely.
3. Use parentheses: Alternatively, you can enclose the repeating digits in parentheses to indicate the repetition. This is commonly used when writing out repeating decimals in a simplified form.
Here's an example to illustrate the process:
Let's say we have the decimal number 0.314159159159159...
- Identifying the repeating pattern: In the above example, the digits 159 repeat in a pattern.
- Placing the repeating pattern over a line: You can write it as 0.314 (overline 159), indicating that the digits 159 repeat indefinitely.
- Using parentheses: Alternatively, you can write it as 0.314(159), where the digits 159 are enclosed in parentheses to indicate the repetition.
Remember to adjust the placement of the repeating pattern based on its position within the decimal number.
To show the group of digits that repeat in a repeating decimal, you can follow these steps:
1. Convert the repeating decimal into a fraction: Determine the repeating portion of the decimal and represent it as a fraction. For example, if the repeating portion is "0.333...", you can represent it as 1/3.
2. Simplify the fraction: Reduce the fraction to its simplest form. Using the previous example, 1/3 is already in its simplest form.
3. Identify the repeating digits: The numerator of the simplified fraction represents the repeating digits in the decimal. In the example of 1/3, the repeating digit is 3.
So, to answer your question, to show the group of digits that repeat in a repeating decimal, you need to convert the repeating decimal into a fraction, simplify it if necessary, and then identify the repeating digits based on the numerator of the fraction.