What is 95.20111... as a Fraction?

95.201 equals 85681900 as a fraction.

How do you turn 95.201 repeating into a fraction?

Detailed Answer:

Step 1: To convert 95.201 repeating into a fraction, begin writing this simple equation:

n = 95.201 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (1) and 2 digits in the non-repeating part (20). Multiply both sides by 10³ = 1000.

1000 × n = 95201.1 (equation 2)

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

1000 × n = 95201.1
 100 × n = 95.201
 900 × n = 85681

n = 85681900 (answer)

95.201 = 85681900 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 85681900 is also equal to 95181900 when expressed as a mixed number.

The repeating decimal 95.201 (vinculum notation) has a repeated block length of 1. It is also represented as 95.20111... (ellipsis notation) which equals approximately 95.2011111 (decimal approximation)(*).

The recurring decimal 95.201 can be written as a ratio of two integers having 85681 as the numerator and 900 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.