What is 1.84545... as a Fraction?

1.845 equals 203110 as a fraction.

How do you turn 1.845 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.845 repeating into a fraction, begin writing this simple equation:

n = 1.845 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (45) and 1 digit in the non-repeating part (8). Multiply both sides by 10³ = 1000.

1000 × n = 1845.45 (equation 2)

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

1000 × n = 1845.45
  10 × n = 1.845
 990 × n = 1827

1827990 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 = 1827990 = 1827 ÷ 9990 ÷ 9 = 203110. So,

1.845 = 203110 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 203110 is also equal to 193110 when expressed as a mixed number.

The repeating decimal 1.845 (vinculum notation) has a repeated block length of 2. It is also represented as 1.8454545... (ellipsis notation) which equals approximately 1.84545454545 (decimal approximation)(*).

The recurring decimal 1.845 can be written as a ratio of two integers having 203 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.