Question

Convert 0.8¯¯¯ to a rational number.(1 point)

Answer 1

How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses

Answer 2

To convert the repeating decimal 0.8¯¯¯ to a rational number, we can set it equal to a variable, x, and multiply both sides of the equation by 10 to eliminate the repeating decimal:

x = 0.8¯¯¯
10x = 8.8¯¯¯

Next, we subtract the original equation from the second equation:

10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8

Finally, we solve for x by dividing both sides of the equation by 9:

x = 8/9

Therefore, the repeating decimal 0.8¯¯¯ can be written as the rational number 8/9.

Answer 3

To show the group of digits that repeat in a repeating decimal, one can use a vinculum (a horizontal bar) placed over the repeating digits. For example, if the digits 3, 4, and 5 repeat in a decimal, it can be represented as 0.345¯¯¯ or as 0.[345]. This notation helps to clearly indicate which digits repeat in the decimal representation.