What is 2.38153153153... as a Fraction?

2.38153 equals 52872220 as a fraction.

How do you turn 2.38153 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.38153 repeating into a fraction, begin writing this simple equation:

n = 2.38153 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (153) and 2 digits in the non-repeating part (38). Multiply both sides by 10⁵ = 100000.

100000 × n = 238153.153 (equation 2)

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

100000 × n = 238153.153
   100 × n = 2.38153
 99900 × n = 237915

23791599900 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 45 (the GCF - greatest common factor).

n = 23791599900 = 237915 ÷ 4599900 ÷ 45 = 52872220. So,

2.38153 = 52872220 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 52872220 is also equal to 28472220 when expressed as a mixed number.

The repeating decimal 2.38153 (vinculum notation) has a repeated block length of 3. It is also represented as 2.38153153153... (ellipsis notation) which equals approximately 2.38153153153153153 (decimal approximation)(*).

The recurring decimal 2.38153 can be written as a ratio of two integers having 5287 as the numerator and 2220 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.