What is the mixed number form of 4.1 with a repeating 66?

Please check your problem.

4.1 = 4 1/10

Well, you know that 1/6 = 0.16666...

so, you have 4 1/6

To find the mixed number form of 4.1 with a repeating 66, we need to convert the repeating decimal into a fraction and then express it as a mixed number.

Step 1: Determine the fraction value of the repeating decimal.
Let's call the repeating decimal x. To convert a repeating decimal into a fraction, we multiply it by a power of 10 that eliminates the repeating part. In this case, we have two digits repeating, so we multiply x by 100 (10^2):
100x = 66.6666...

Step 2: Subtract the original equation from the equation obtained in Step 1.
Since the repeating part has recurring 6s, we can subtract the original equation from the equation obtained in Step 1 to eliminate the repeating part:
100x - x = 66.6666... - 4.1

Simplifying the equation:
99x = 62.5666...

Step 3: Solve for x.
To solve for x, we divide both sides of the equation by 99:
x = (62.5666...)/99

Step 4: Convert x into a fraction.
Since x is a repeating decimal, we can write it as a fraction by placing the repeating part over a series of 9s equal to the number of repeating digits. In this case, we have two repeating 6s, so we put 66 over 99:
x = 66/99

Step 5: Simplify the fraction, if possible.
Both the numerator (66) and the denominator (99) have a common factor of 33. By dividing both by 33, we get the simplified fraction:
x = 2/3

Step 6: Express the mixed number form.
To express 4.1 with a repeating 66 as a mixed number, we combine the whole number part (4) with the fraction part (2/3):
4 2/3

Therefore, the mixed number form of 4.1 with a repeating 66 is 4 2/3.