What is 45.19444... as a Fraction?

45.194 equals 162736 as a fraction.

How do you turn 45.194 repeating into a fraction?

Detailed Answer:

Step 1: To convert 45.194 repeating into a fraction, begin writing this simple equation:

n = 45.194 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (4) and 2 digits in the non-repeating part (19). Multiply both sides by 10³ = 1000.

1000 × n = 45194.4 (equation 2)

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

1000 × n = 45194.4
 100 × n = 45.194
 900 × n = 40675

40675900 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 25 (the GCF - greatest common factor).

n = 40675900 = 40675 ÷ 25900 ÷ 25 = 162736. So,

45.194 = 162736 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 162736 is also equal to 45736 when expressed as a mixed number.

The repeating decimal 45.194 (vinculum notation) has a repeated block length of 1. It is also represented as 45.19444... (ellipsis notation) which equals approximately 45.1944444 (decimal approximation)(*).

The recurring decimal 45.194 can be written as a ratio of two integers having 1627 as the numerator and 36 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.