express 8/11 as a repeating decimal
To express 8/11 as a repeating decimal, you need to perform long division. Here's how:
0.
___________________________
11 | 8.000000000000000
- 7.3 0
________________
2.7000000000
- 2.7000
_______________
0.0
As we can see, the remainder becomes 0, so the decimal terminates. Therefore, 8/11 = 0.72.
To express 8/11 as a repeating decimal, follow these steps:
Step 1: Divide the numerator (8) by the denominator (11).
8 ÷ 11 = 0.727272...
Step 2: Since the remainder is 8, write down the numerator (8) and add a decimal point after it.
8.
Step 3: Multiply the remainder (8) by 10 and divide it by the denominator (11).
(8 × 10) ÷ 11 = 72 ÷ 11 = 6 remainder 6
Step 4: Write down the remainder (6) obtained in Step 3 and put it after the decimal point.
8.6
Step 5: Repeat steps 3 and 4 until a pattern emerges or you achieve the desired accuracy.
(6 × 10) ÷ 11 = 60 ÷ 11 = 5 remainder 5
(5 × 10) ÷ 11 = 50 ÷ 11 = 4 remainder 6
(6 × 10) ÷ 11 = 60 ÷ 11 = 5 remainder 5
Step 6: As a pattern has emerged, the repeating decimal representation of 8/11 is:
0.72(72)