What is 158.9777... as a Fraction?

158.97 equals 715445 as a fraction.

How do you turn 158.97 repeating into a fraction?

Detailed Answer:

Step 1: To convert 158.97 repeating into a fraction, begin writing this simple equation:

n = 158.97 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7) and 1 digit in the non-repeating part (9). Multiply both sides by 10² = 100.

100 × n = 15897.7 (equation 2)

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

100 × n = 15897.7
 10 × n = 158.97
 90 × n = 14308

1430890 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 2 (the GCF - greatest common factor).

n = 1430890 = 14308 ÷ 290 ÷ 2 = 715445. So,

158.97 = 715445 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 715445 is also equal to 1584445 when expressed as a mixed number.

The repeating decimal 158.97 (vinculum notation) has a repeated block length of 1. It is also represented as 158.9777... (ellipsis notation) which equals approximately 158.977777 (decimal approximation)(*).

The recurring decimal 158.97 can be written as a ratio of two integers having 7154 as the numerator and 45 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.