What is 10.70101... as a Fraction?

10.701 equals 5297495 as a fraction.

How do you turn 10.701 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.701 repeating into a fraction, begin writing this simple equation:

n = 10.701 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (01) and 1 digit in the non-repeating part (7). Multiply both sides by 10³ = 1000.

1000 × n = 10701.01 (equation 2)

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

1000 × n = 10701.01
  10 × n = 10.701
 990 × n = 10594

10594990 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 2 (the GCF - greatest common factor).

n = 10594990 = 10594 ÷ 2990 ÷ 2 = 5297495. So,

10.701 = 5297495 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 5297495 is also equal to 10347495 when expressed as a mixed number.

The repeating decimal 10.701 (vinculum notation) has a repeated block length of 2. It is also represented as 10.7010101... (ellipsis notation) which equals approximately 10.70101010101 (decimal approximation)(*).

The recurring decimal 10.701 can be written as a ratio of two integers having 5297 as the numerator and 495 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.