What is 35.133... as a Fraction?

35.13 equals 52715 as a fraction.

How do you turn 35.13 repeating into a fraction?

Detailed Answer:

Step 1: To convert 35.13 repeating into a fraction, begin writing this simple equation:

n = 35.13 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 1 digit in the non-repeating part (1). Multiply both sides by 10² = 100.

100 × n = 3513.3 (equation 2)

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

100 × n = 3513.3
 10 × n = 35.13
 90 × n = 3162

316290 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 6 (the GCF - greatest common factor).

n = 316290 = 3162 ÷ 690 ÷ 6 = 52715. So,

35.13 = 52715 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 52715 is also equal to 35215 when expressed as a mixed number.

The repeating decimal 35.13 (vinculum notation) has a repeated block length of 1. It is also represented as 35.1333... (ellipsis notation) which equals approximately 35.133333 (decimal approximation)(*).

The recurring decimal 35.13 can be written as a ratio of two integers having 527 as the numerator and 15 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.