What is 29.13888... as a Fraction?

29.138 equals 104936 as a fraction.

How do you turn 29.138 repeating into a fraction?

Detailed Answer:

Step 1: To convert 29.138 repeating into a fraction, begin writing this simple equation:

n = 29.138 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (13). Multiply both sides by 10³ = 1000.

1000 × n = 29138.8 (equation 2)

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

1000 × n = 29138.8
 100 × n = 29.138
 900 × n = 26225

26225900 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 25 (the GCF - greatest common factor).

n = 26225900 = 26225 ÷ 25900 ÷ 25 = 104936. So,

29.138 = 104936 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 104936 is also equal to 29536 when expressed as a mixed number.

The repeating decimal 29.138 (vinculum notation) has a repeated block length of 1. It is also represented as 29.13888... (ellipsis notation) which equals approximately 29.1388888 (decimal approximation)(*).

The recurring decimal 29.138 can be written as a ratio of two integers having 1049 as the numerator and 36 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.