What is 0.1515... as a Fraction?

0.15 equals 533 as a fraction.

How do you turn 0.15 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.15 repeating into a fraction, begin writing this simple equation:

n = 0.15 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (15), so multiply both sides by 10² = 100.

100 × n = 15.15 (equation 2)

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

100 × n = 15.15
  1 × n = 0.15
 99 × n = 15

1599 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 3 (the GCF - greatest common factor).

n = 1599 = 15 ÷ 399 ÷ 3 = 533. So,

0.15 = 533 as the lowest possible fraction.

The repeating decimal 0.15 (vinculum notation) has a repeated block length of 2. It is also represented as 0.151515... (ellipsis notation) which equals approximately 0.1515151515 (decimal approximation)(*).

The recurring decimal 0.15 can be written as a ratio of two integers having 5 as the numerator and 33 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.