What is 9.72222... as a Fraction?

9.722 equals 17518 as a fraction.

How do you turn 9.722 repeating into a fraction?

Detailed Answer:

Step 1: To convert 9.722 repeating into a fraction, begin writing this simple equation:

n = 9.722 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 2 digits in the non-repeating part (72). Multiply both sides by 10³ = 1000.

1000 × n = 9722.2 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

1000 × n = 9722.2
 100 × n = 9.722
 900 × n = 8750

8750900 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 50 (the GCF - greatest common factor).

n = 8750900 = 8750 ÷ 50900 ÷ 50 = 17518. So,

9.722 = 17518 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 17518 is also equal to 91318 when expressed as a mixed number.

The repeating decimal 9.722 (vinculum notation) has a repeated block length of 1. It is also represented as 9.72222... (ellipsis notation) which equals approximately 9.7222222 (decimal approximation)(*).

The recurring decimal 9.722 can be written as a ratio of two integers having 175 as the numerator and 18 as the denominator. So, it is a rational number (named after ratio). It can be shown that a number is rational if its decimal representation is repeating or terminating.

(*) At present, there is no single universally accepted notation or phrasing for repeating decimals.