What is 7.152828... as a Fraction?

7.1528 equals 708139900 as a fraction.

How do you turn 7.1528 repeating into a fraction?

Detailed Answer:

Step 1: To convert 7.1528 repeating into a fraction, begin writing this simple equation:

n = 7.1528 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (28) and 2 digits in the non-repeating part (15). Multiply both sides by 10⁴ = 10000.

10000 × n = 71528.28 (equation 2)

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

10000 × n = 71528.28
  100 × n = 7.1528
 9900 × n = 70813

n = 708139900 (answer)

7.1528 = 708139900 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 708139900 is also equal to 715139900 when expressed as a mixed number.

The repeating decimal 7.1528 (vinculum notation) has a repeated block length of 2. It is also represented as 7.15282828... (ellipsis notation) which equals approximately 7.152828282828 (decimal approximation)(*).

The recurring decimal 7.1528 can be written as a ratio of two integers having 70813 as the numerator and 9900 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.