What is 10.15153153153... as a Fraction?

10.15153 equals 563415550 as a fraction.

How do you turn 10.15153 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.15153 repeating into a fraction, begin writing this simple equation:

n = 10.15153 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (153) and 2 digits in the non-repeating part (15). Multiply both sides by 10⁵ = 100000.

100000 × n = 1015153.153 (equation 2)

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

100000 × n = 1015153.153
   100 × n = 10.15153
 99900 × n = 1014138

101413899900 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 18 (the GCF - greatest common factor).

n = 101413899900 = 1014138 ÷ 1899900 ÷ 18 = 563415550. So,

10.15153 = 563415550 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 563415550 is also equal to 108415550 when expressed as a mixed number.

The repeating decimal 10.15153 (vinculum notation) has a repeated block length of 3. It is also represented as 10.15153153153... (ellipsis notation) which equals approximately 10.15153153153153153 (decimal approximation)(*).

The recurring decimal 10.15153 can be written as a ratio of two integers having 56341 as the numerator and 5550 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.