Answer:
the repeating decimal 7.45454545... can be written as the mixed number 7 5/11 in its simplest form.
Explanation:
To convert the repeating decimal 7.45 into a mixed number, we need to find the fraction that it represents.
Let x = 7.45454545...
Then 100x = 745.45454545...
Subtracting x from 100x gives:
99x = 738
So, x = 738/99
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 3:
738/99 = (3 x 246)/(3 x 33) = 246/33
Now, we can write 246/33 as a mixed number:
246/33 = 7 and 15/33
We can simplify the fraction 15/33 by dividing both the numerator and the denominator by their greatest common factor, which is 3:
15/33 = (3 x 5)/(3 x 11) = 5/11
So, the mixed number in its simplest form is:
7 5/11
Therefore, the repeating decimal 7.45454545... can be written as the mixed number 7 5/11 in its simplest form.