What is 1.1757575... as a Fraction?

1.175 equals 194165 as a fraction.

How do you turn 1.175 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.175 repeating into a fraction, begin writing this simple equation:

n = 1.175 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (75) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 1175.75 (equation 2)

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

1000 × n = 1175.75
  10 × n = 1.175
 990 × n = 1164

1164990 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 6 (the GCF - greatest common factor).

n = 1164990 = 1164 ÷ 6990 ÷ 6 = 194165. So,

1.175 = 194165 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 194165 is also equal to 129165 when expressed as a mixed number.

The repeating decimal 1.175 (vinculum notation) has a repeated block length of 2. It is also represented as 1.1757575... (ellipsis notation) which equals approximately 1.17575757575 (decimal approximation)(*).

The recurring decimal 1.175 can be written as a ratio of two integers having 194 as the numerator and 165 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.