Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
To express 7/13 as a repeating decimal, you divide 7 by 13:
7 ÷ 13 = 0.538461538461...
To indicate the repeating digits with a bar, the result is 0.538461 with the digits 538461 repeating indefinitely. So the decimal representation of 7/13 is 0.538461̅.
To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 100 since 0.82¯¯¯¯¯ has two repeating digits.
Convert 0.8¯¯¯ to a rational number.
To convert 0.8¯¯¯ to a rational number, we can assign the repeating portion to a variable, let's say x:
x = 0.8¯¯¯
Now, to eliminate the repeating part, we can multiply both sides of the equation by 10 to move the decimal point one place to the right:
10x = 8.¯¯¯
Next, subtract the original equation from the one above:
10x - x = 8.¯¯¯ - 0.8¯¯¯
9x = 8
Solving for x:
x = 8/9
Therefore, 0.8¯¯¯ as a rational number is 8/9.