What is 70.13888... as a Fraction?

70.138 equals 252536 as a fraction.

How do you turn 70.138 repeating into a fraction?

Detailed Answer:

Step 1: To convert 70.138 repeating into a fraction, begin writing this simple equation:

n = 70.138 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (13). Multiply both sides by 10³ = 1000.

1000 × n = 70138.8 (equation 2)

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

1000 × n = 70138.8
 100 × n = 70.138
 900 × n = 63125

63125900 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 25 (the GCF - greatest common factor).

n = 63125900 = 63125 ÷ 25900 ÷ 25 = 252536. So,

70.138 = 252536 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 252536 is also equal to 70536 when expressed as a mixed number.

The repeating decimal 70.138 (vinculum notation) has a repeated block length of 1. It is also represented as 70.13888... (ellipsis notation) which equals approximately 70.1388888 (decimal approximation)(*).

The recurring decimal 70.138 can be written as a ratio of two integers having 2525 as the numerator and 36 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.