What is 10.02727... as a Fraction?

10.27 equals 1103110 as a fraction.

How do you turn 10.27 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.27 repeating into a fraction, begin writing this simple equation:

n = 10.27 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (27), so multiply both sides by 10² = 100.

100 × n = 1027.27 (equation 2)

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

100 × n = 1027.27
  1 × n = 10.27
 99 × n = 1017

101799 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 = 101799 = 1017 ÷ 999 ÷ 9 = 1103110. So,

10.27 = 1103110 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 1103110 is also equal to 103110 when expressed as a mixed number.

The repeating decimal 10.27 (vinculum notation) has a repeated block length of 2. It is also represented as 10.272727... (ellipsis notation) which equals approximately 10.2727272727 (decimal approximation)(*).

The recurring decimal 10.27 can be written as a ratio of two integers having 1103 as the numerator and 110 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.