Express (8)/(11) as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express (8)/(11) as a repeating decimal, we need to divide 8 by 11.
Upon division, we get:
0.727272...
The cycle of repeating digits is 27.
So, (8)/(11) as a repeating decimal is expressed as 0.72¯¯¯¯¯.
To express the fraction (8)/(11) as a repeating decimal, you can use long division. Here's the step-by-step process:
1. Start by dividing 8 by 11: 8 ÷ 11 = 0.72.
2. Since the division did not result in a whole number, place a decimal point after 0: 0.
3. Bring down the next digit of the dividend (which is 0): 0 ÷ 11 = 0.
4. Multiply the current quotient (0) by 10: 0 × 10 = 0.
5. Subtract the product from step 4 from the current dividend (0): 0 - 0 = 0.
6. Bring down the next digit of the dividend (which is 0): 0 ÷ 11 = 0.
7. Repeat steps 4-6 until either the remainder becomes 0 or you notice a repeating pattern.
The division process will continue indefinitely with zeros as the remainder, indicating that the decimal representation of (8)/(11) is a repeating decimal. The pattern will start repeating from the very beginning, so we can write it as 0.72 with a bar over the 72, indicating that the digits 72 repeat.
Therefore, (8)/(11) can be expressed as 0.72̅.
To express the fraction (8)/(11) as a repeating decimal, you can use long division. Here's how:
1. Divide 8 by 11: 8 ÷ 11 = 0 with a remainder of 8.
2. Add a decimal point after the 0 in the quotient, which gives us 0.
3. Since we have a remainder, bring down a zero after the 8 in the dividend: 80.
4. Divide 80 by 11: 80 ÷ 11 = 7 with a remainder of 3.
5. Divide 30 by 11: 30 ÷ 11 = 2 with a remainder of 8.
6. Repeat the process by bringing down another zero after the remainder. We have 80 again.
7. Divide 80 by 11: 80 ÷ 11 = 7 with a remainder of 3.
At this point, you can see a repeating pattern emerge. The remainder 3 repeats continuously. Therefore, the fraction (8)/(11) as a repeating decimal is approximately 0.727272... where the cycle of repeating digits (27) is marked with a bar over them.