What is 29.0777... as a Fraction?

29.7 equals 261790 as a fraction.

How do you turn 29.7 repeating into a fraction?

Detailed Answer:

Step 1: To convert 29.7 repeating into a fraction, begin writing this simple equation:

n = 29.7 (equation 1)

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

10 × n = 297.7 (equation 2)

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

10 × n = 297.7
 1 × n = 29.7
 9 × n = 268

n = 261790 (answer)

29.7 = 261790 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 261790 is also equal to 29790 when expressed as a mixed number.

The repeating decimal 29.7 (vinculum notation) has a repeated block length of 1. It is also represented as 29.777... (ellipsis notation) which equals approximately 29.77777 (decimal approximation)(*).

The recurring decimal 29.7 can be written as a ratio of two integers having 2617 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.