What is 3.1787878... as a Fraction?

3.178 equals 1049330 as a fraction.

How do you turn 3.178 repeating into a fraction?

Detailed Answer:

Step 1: To convert 3.178 repeating into a fraction, begin writing this simple equation:

n = 3.178 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (78) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 3178.78 (equation 2)

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

1000 × n = 3178.78
  10 × n = 3.178
 990 × n = 3147

3147990 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 = 3147990 = 3147 ÷ 3990 ÷ 3 = 1049330. So,

3.178 = 1049330 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 1049330 is also equal to 359330 when expressed as a mixed number.

The repeating decimal 3.178 (vinculum notation) has a repeated block length of 2. It is also represented as 3.1787878... (ellipsis notation) which equals approximately 3.17878787878 (decimal approximation)(*).

The recurring decimal 3.178 can be written as a ratio of two integers having 1049 as the numerator and 330 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.