What is 45.3444... as a Fraction?

45.34 equals 408190 as a fraction.

How do you turn 45.34 repeating into a fraction?

Detailed Answer:

Step 1: To convert 45.34 repeating into a fraction, begin writing this simple equation:

n = 45.34 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (4) and 1 digit in the non-repeating part (3). Multiply both sides by 10² = 100.

100 × n = 4534.4 (equation 2)

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

100 × n = 4534.4
 10 × n = 45.34
 90 × n = 4081

n = 408190 (answer)

45.34 = 408190 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 408190 is also equal to 453190 when expressed as a mixed number.

The repeating decimal 45.34 (vinculum notation) has a repeated block length of 1. It is also represented as 45.3444... (ellipsis notation) which equals approximately 45.344444 (decimal approximation)(*).

The recurring decimal 45.34 can be written as a ratio of two integers having 4081 as the numerator and 90 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.