What is 345.233... as a Fraction?

345.233 equals 1035730 as a fraction.

How do you turn 345.233 repeating into a fraction?

Detailed Answer:

Step 1: To convert 345.233 repeating into a fraction, begin writing this simple equation:

n = 345.233 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (23). Multiply both sides by 10³ = 1000.

1000 × n = 345233.3 (equation 2)

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

1000 × n = 345233.3
 100 × n = 345.233
 900 × n = 310710

310710900 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 30 (the GCF - greatest common factor).

n = 310710900 = 310710 ÷ 30900 ÷ 30 = 1035730. So,

345.233 = 1035730 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 1035730 is also equal to 345730 when expressed as a mixed number.

The repeating decimal 345.233 (vinculum notation) has a repeated block length of 1. It is also represented as 345.23333... (ellipsis notation) which equals approximately 345.2333333 (decimal approximation)(*).

The recurring decimal 345.233 can be written as a ratio of two integers having 10357 as the numerator and 30 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.