What is 174.6777... as a Fraction?

174.67 equals 1572190 as a fraction.

How do you turn 174.67 repeating into a fraction?

Detailed Answer:

Step 1: To convert 174.67 repeating into a fraction, begin writing this simple equation:

n = 174.67 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7) and 1 digit in the non-repeating part (6). Multiply both sides by 10² = 100.

100 × n = 17467.7 (equation 2)

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

100 × n = 17467.7
 10 × n = 174.67
 90 × n = 15721

n = 1572190 (answer)

174.67 = 1572190 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 1572190 is also equal to 1746190 when expressed as a mixed number.

The repeating decimal 174.67 (vinculum notation) has a repeated block length of 1. It is also represented as 174.6777... (ellipsis notation) which equals approximately 174.677777 (decimal approximation)(*).

The recurring decimal 174.67 can be written as a ratio of two integers having 15721 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.