What is 1.114666... as a Fraction?

1.1146 equals 418375 as a fraction.

How do you turn 1.1146 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.1146 repeating into a fraction, begin writing this simple equation:

n = 1.1146 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 3 digits in the non-repeating part (114). Multiply both sides by 10⁴ = 10000.

10000 × n = 11146.6 (equation 2)

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

10000 × n = 11146.6
 1000 × n = 1.1146
 9000 × n = 10032

100329000 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 24 (the GCF - greatest common factor).

n = 100329000 = 10032 ÷ 249000 ÷ 24 = 418375. So,

1.1146 = 418375 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 418375 is also equal to 143375 when expressed as a mixed number.

The repeating decimal 1.1146 (vinculum notation) has a repeated block length of 1. It is also represented as 1.114666... (ellipsis notation) which equals approximately 1.11466666 (decimal approximation)(*).

The recurring decimal 1.1146 can be written as a ratio of two integers having 418 as the numerator and 375 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.