Question

what is the decimal form of \\(\frac{4}{11}\\)? 0.363636... 0.363666... 0.363636 0.3636

Explanation:

Step1: Divide 4 by 11

To find the decimal form of \(\frac{4}{11}\), we perform long division. \(4\div11\) gives a repeating decimal.
When we divide 4 by 11:

• \(11\) goes into \(40\) three times (\(3\times11 = 33\)), with a remainder of \(40 - 33=7\).
• Bring down a 0: \(70\). \(11\) goes into \(70\) six times (\(6\times11 = 66\)), remainder \(70 - 66 = 4\).
• Now we see the remainder is \(4\), which is the same as the original dividend's numerator, so the decimal repeats.

So, \(4\div11 = 0.363636\cdots\)

Step2: Match with the options

Looking at the options, the repeating decimal \(0.363636\cdots\) is one of the choices.

Answer:

0.363636...