What is 49.777... as a Fraction?

49.7 equals 4489 as a fraction.

How do you turn 49.7 repeating into a fraction?

Detailed Answer:

Step 1: To convert 49.7 repeating into a fraction, begin writing this simple equation:

n = 49.7 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7), so multiply both sides by 10¹ = 10.

10 × n = 497.7 (equation 2)

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

10 × n = 497.7
 1 × n = 49.7
 9 × n = 448

n = 4489 (answer)

49.7 = 4489 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 4489 is also equal to 4979 when expressed as a mixed number.

The repeating decimal 49.7 (vinculum notation) has a repeated block length of 1. It is also represented as 49.777... (ellipsis notation) which equals approximately 49.77777 (decimal approximation)(*).

The recurring decimal 49.7 can be written as a ratio of two integers having 448 as the numerator and 9 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.