What is 10.96666... as a Fraction?

10.966 equals 32930 as a fraction.

How do you turn 10.966 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.966 repeating into a fraction, begin writing this simple equation:

n = 10.966 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 2 digits in the non-repeating part (96). Multiply both sides by 10³ = 1000.

1000 × n = 10966.6 (equation 2)

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

1000 × n = 10966.6
 100 × n = 10.966
 900 × n = 9870

9870900 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 30 (the GCF - greatest common factor).

n = 9870900 = 9870 ÷ 30900 ÷ 30 = 32930. So,

10.966 = 32930 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 32930 is also equal to 102930 when expressed as a mixed number.

The repeating decimal 10.966 (vinculum notation) has a repeated block length of 1. It is also represented as 10.96666... (ellipsis notation) which equals approximately 10.9666666 (decimal approximation)(*).

The recurring decimal 10.966 can be written as a ratio of two integers having 329 as the numerator and 30 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.