Answer :
A mixed fraction for the given repeating decimal is 3 17/99.
The given decimal is $3.171717.
We need to write the repeating decimal cost as a fraction and as a mixed number.
How do convert repeating decimals to fractions?
The repeating decimal to fraction steps of conversion are given below:
Step 1: Identify the repeating digits in the given decimal number.
Step 2: Equate the decimal number with x or any other variable.
Step 3: Place the repeating digits to the left of the decimal point by multiplying the equation obtained in step 2 by a power of 10 equal to the number of repeating digits. This way you will get another equation.
Step 4: Subtract the equation obtained in step 2 from the equation obtained in step 3.
Step 5: Simplify to get the answer.
Now, in the given decimal 2 digits are repeating.
Take, x=3.171717.....--------(1)
Multiply both sides of the equation by 100.
That is, 100x=317.1717.....--------(2)
Subtract equation (1) from equation (2)
100x-x=317.1717.....-3.171717.....
⇒99x=314
⇒x=314/99
⇒x=3 17/99
Therefore, a mixed fraction for the given repeating decimal is 3 17/99.
To learn more about the conversion of repeating decimal and mixed fractions visit:
https://brainly.com/question/4735051.
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