What is 0.1706060606... as a Fraction?

0.1706 equals 5633300 as a fraction.

How do you turn 0.1706 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1706 repeating into a fraction, begin writing this simple equation:

n = 0.1706 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (06) and 2 digits in the non-repeating part (17). Multiply both sides by 10⁴ = 10000.

10000 × n = 1706.06 (equation 2)

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

10000 × n = 1706.06
  100 × n = 0.1706
 9900 × n = 1689

16899900 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 = 16899900 = 1689 ÷ 39900 ÷ 3 = 5633300. So,

0.1706 = 5633300 as the lowest possible fraction.

The repeating decimal 0.1706 (vinculum notation) has a repeated block length of 2. It is also represented as 0.17060606... (ellipsis notation) which equals approximately 0.170606060606 (decimal approximation)(*).

The recurring decimal 0.1706 can be written as a ratio of two integers having 563 as the numerator and 3300 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.