What is 159.6777... as a Fraction?

159.67 equals 1437190 as a fraction.

How do you turn 159.67 repeating into a fraction?

Detailed Answer:

Step 1: To convert 159.67 repeating into a fraction, begin writing this simple equation:

n = 159.67 (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 = 15967.7 (equation 2)

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

100 × n = 15967.7
 10 × n = 159.67
 90 × n = 14371

n = 1437190 (answer)

159.67 = 1437190 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 1437190 is also equal to 1596190 when expressed as a mixed number.

The repeating decimal 159.67 (vinculum notation) has a repeated block length of 1. It is also represented as 159.6777... (ellipsis notation) which equals approximately 159.677777 (decimal approximation)(*).

The recurring decimal 159.67 can be written as a ratio of two integers having 14371 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.