What is 1.29153153153... as a Fraction?

1.29153 equals 35842775 as a fraction.

How do you turn 1.29153 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.29153 repeating into a fraction, begin writing this simple equation:

n = 1.29153 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (153) and 2 digits in the non-repeating part (29). Multiply both sides by 10⁵ = 100000.

100000 × n = 129153.153 (equation 2)

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

100000 × n = 129153.153
   100 × n = 1.29153
 99900 × n = 129024

12902499900 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 36 (the GCF - greatest common factor).

n = 12902499900 = 129024 ÷ 3699900 ÷ 36 = 35842775. So,

1.29153 = 35842775 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 35842775 is also equal to 18092775 when expressed as a mixed number.

The repeating decimal 1.29153 (vinculum notation) has a repeated block length of 3. It is also represented as 1.29153153153... (ellipsis notation) which equals approximately 1.29153153153153153 (decimal approximation)(*).

The recurring decimal 1.29153 can be written as a ratio of two integers having 3584 as the numerator and 2775 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.