What is 14.70666... as a Fraction?

14.706 equals 110375 as a fraction.

How do you turn 14.706 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.706 repeating into a fraction, begin writing this simple equation:

n = 14.706 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 2 digits in the non-repeating part (70). Multiply both sides by 10³ = 1000.

1000 × n = 14706.6 (equation 2)

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

1000 × n = 14706.6
 100 × n = 14.706
 900 × n = 13236

13236900 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 12 (the GCF - greatest common factor).

n = 13236900 = 13236 ÷ 12900 ÷ 12 = 110375. So,

14.706 = 110375 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 110375 is also equal to 145375 when expressed as a mixed number.

The repeating decimal 14.706 (vinculum notation) has a repeated block length of 1. It is also represented as 14.70666... (ellipsis notation) which equals approximately 14.7066666 (decimal approximation)(*).

The recurring decimal 14.706 can be written as a ratio of two integers having 1103 as the numerator and 75 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.