What is 1.197171... as a Fraction?

1.1971 equals 29632475 as a fraction.

How do you turn 1.1971 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.1971 repeating into a fraction, begin writing this simple equation:

n = 1.1971 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (71) and 2 digits in the non-repeating part (19). Multiply both sides by 10⁴ = 10000.

10000 × n = 11971.71 (equation 2)

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

10000 × n = 11971.71
  100 × n = 1.1971
 9900 × n = 11852

118529900 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 4 (the GCF - greatest common factor).

n = 118529900 = 11852 ÷ 49900 ÷ 4 = 29632475. So,

1.1971 = 29632475 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 29632475 is also equal to 14882475 when expressed as a mixed number.

The repeating decimal 1.1971 (vinculum notation) has a repeated block length of 2. It is also represented as 1.19717171... (ellipsis notation) which equals approximately 1.197171717171 (decimal approximation)(*).

The recurring decimal 1.1971 can be written as a ratio of two integers having 2963 as the numerator and 2475 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.