What is 337.1633... as a Fraction?

337.163 equals 101149300 as a fraction.

How do you turn 337.163 repeating into a fraction?

Detailed Answer:

Step 1: To convert 337.163 repeating into a fraction, begin writing this simple equation:

n = 337.163 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (16). Multiply both sides by 10³ = 1000.

1000 × n = 337163.3 (equation 2)

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

1000 × n = 337163.3
 100 × n = 337.163
 900 × n = 303447

303447900 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 3 (the GCF - greatest common factor).

n = 303447900 = 303447 ÷ 3900 ÷ 3 = 101149300. So,

337.163 = 101149300 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 101149300 is also equal to 33749300 when expressed as a mixed number.

The repeating decimal 337.163 (vinculum notation) has a repeated block length of 1. It is also represented as 337.16333... (ellipsis notation) which equals approximately 337.1633333 (decimal approximation)(*).

The recurring decimal 337.163 can be written as a ratio of two integers having 101149 as the numerator and 300 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.