What is 0.10153153153... as a Fraction?

0.10153 equals 112711100 as a fraction.

How do you turn 0.10153 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.10153 repeating into a fraction, begin writing this simple equation:

n = 0.10153 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (153) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁵ = 100000.

100000 × n = 10153.153 (equation 2)

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

100000 × n = 10153.153
   100 × n = 0.10153
 99900 × n = 10143

1014399900 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 9 (the GCF - greatest common factor).

n = 1014399900 = 10143 ÷ 999900 ÷ 9 = 112711100. So,

0.10153 = 112711100 as the lowest possible fraction.

The repeating decimal 0.10153 (vinculum notation) has a repeated block length of 3. It is also represented as 0.10153153153... (ellipsis notation) which equals approximately 0.10153153153153153 (decimal approximation)(*).

The recurring decimal 0.10153 can be written as a ratio of two integers having 1127 as the numerator and 11100 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.