What is 5.134333... as a Fraction?

5.1343 equals 154033000 as a fraction.

How do you turn 5.1343 repeating into a fraction?

Detailed Answer:

Step 1: To convert 5.1343 repeating into a fraction, begin writing this simple equation:

n = 5.1343 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 3 digits in the non-repeating part (134). Multiply both sides by 10⁴ = 10000.

10000 × n = 51343.3 (equation 2)

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

10000 × n = 51343.3
 1000 × n = 5.1343
 9000 × n = 46209

462099000 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 = 462099000 = 46209 ÷ 39000 ÷ 3 = 154033000. So,

5.1343 = 154033000 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 154033000 is also equal to 54033000 when expressed as a mixed number.

The repeating decimal 5.1343 (vinculum notation) has a repeated block length of 1. It is also represented as 5.134333... (ellipsis notation) which equals approximately 5.13433333 (decimal approximation)(*).

The recurring decimal 5.1343 can be written as a ratio of two integers having 15403 as the numerator and 3000 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.